LB 

1131 
B28 


[BRARY 


THE  UNIVERSITY 
OF  CALIFORNIA 

SANTA  BARBARA 


PRESENTED  BY 

Frances   Hoi  den 


UNIVERSITY  OF  IOWA  STUDIES 
IN  CHILD  WELFARE 

PROFESSOR  BIRD  T.  BALDWIN,  PH.  D.,  EDITOR 


FROM  THE  IOWA  CHILD  WELFARE  RESEARCH  STATION 


VOLUME  II  NUMBER  1 


MENTAL  GROWTH  CURVE  OF 


NORMAL  AND  SUPERIOR 


CH]  LDREN 


STUDIED   BY  MEANS  OF  CONSECUTIVE 
INTELLIGENCE  EXAMINATIONS 

BY 

BIRD  T.  BALDWIN 

AND 
LORLE  I.  STECHER 


PUBLISHED  BY  THE  UNIVERSITY,  IOWA  CITY 


tj.ivo.1  i  i    \jr    \jjt\Ljir  \J 

SANTA  BARBARA 


CONTENTS 


I.  THE  MENTAL  GROWTH  CUBVE 5 

1.  Statement   of  the   Problem. 5 

2.  Data  for  this  study 6 

Chart  I.    Typical  Record  Card  for  Successive  Examinations.  6 

3.  Method  of  Determining  the  Mental  Growth  Curve 8 

4.  The  Analysis  of  the   Mental  Growth   Curve 10 

Table  I.    Mean  Mental  Age  in  Months  of  Superior  and  Aver- 
age Boys  and  Girls  for  Successive  Chronological  Ages....  10 

Chart   II.    Mental   Growth   Curves   for    Superior   and   Aver- 
age Children    11 

Chart  III.    Growth  Curves  in  Height 13 

Table  II.    Mean  Intelligence  Quotients  of  Superior  and  Aver- 
age Boys  and  Girls  for  Successive  Chronological  Ages 14 

5.  The  Analysis  of  the  I.  Q.  Curve 14 

6.  The  Analysis  of  the  Curve  of  the  Rate  of  Mental  Growth  15 
Chart  IV.    I.  Q.  Curves  of  Superior  and  Average  Children..  15 
Table  III.    Mean  Rate  of  Mental  Growth  of  Superior  and 

Average  Boys  and  Girls  for  Chronological  Age  Intervals..  15 
Chart  V.    Rate  of  Mental  Growth  for  Superior  and  Average 

Children 16 

7.  Mean  Group  Differences  at  Successive  Examinations 17 

8.  Discussion    and   Literature    18 

Table   IV.    Mean    Intelligence    Quotients   at   Successive   Ex- 
aminations      18 

Table   V.    Mean   Chronological  Age   and   Mean   Interval  be- 
tween Successive  Examinations    19 

9.  Summary  and   Conclusions    22 

II.  THE  POSSIBILITY  OF  PREDICTION  OF  MENTAL  GROWTH 23 

1.  Intelligence  Status  of  Individuals  at  Successive  Examina- 
tions      23 

Table  VI.    Original  Data  Arranged  in  Order  of  Mean  I.  Q. 

—Boys    24 

Table  VII.    Original  Data  Arranged  in  Order  of  Mean  I.  Q. 

—Girls    30 

2.  Deviation  of  Individuals  from  their  Mean  I.  Q.  Level 36 

Chart  Vla-VIb  Successive  I.  Q.'s 36,  37 

Table  VIII.     Mean   Individual  Deviations  from  Intelligence 

Quotient    Level    37 

Chart  VII.    Individual  I.  Q.  Curves  for  Boys 38 

Chart  VIII.    Individual   I.  Q.   Curves  for  Girls 38 


4  CONTENTS 

3.  Differences  in  I.  Q.  at  Successive  Examinations 39 

Table   IX.       Percentage   Distribution   of  the   Differences   in 

Intelligence    Quotients    40 

Chart    IX.    Percentage    Distribution    of    the    Differences    in 
I.   Q 41 

4.  Intercorrelations    43 

Table    X.    Intercorrelations    of    Intelligence    Quotients,    for 

Two,  Three,  Four,  and  Five  Examination  Groups 45 

Table  XI.     Percentage  of  Children  Tested  by  Same  Examiner  45 

5.  The  Probable  Error  of  Estimate 46 

Table  XII.    Differences  between  the  Obtained  and  Predicted 

Intelligence    Quotients    on    Second,    Third,    Fourth,    and 

Fifth  Examinations  47 

Table  XIII.  Distribution  of  Differences  between  Obtained 

and  Predicted  I.  Q.'s 48 

Chart  X:  Distribution  of  Differences  between  Obtained  and 

Predicted    I.   Q.'s    49 

6.  Summary   and    Conclusions 52 

III.  THE  RELATION  BETWEEN1  PHYSICAL  AND  MENTAL  GROWTH 53 

1.  Data    53 

2.  Resemblances  in  the  Mental  and  Physical  Development  of 
Brothers  and   Sisters    53 

Chart  XI.    Individual  Mental  Growth  Curves  of  Brothers  and 
Sisters    54 

3.  Mean  Mental  Age  of  Physiologically  Accelerated  and  Re- 
tarded  Children    55 

Chart  XIV.    Mean  Mental  Age  in  Months  of  Physiologically 
Accelerated  and  Retarded  Boys  and   Girls 55 

4.  The  Relation  between  Physical  Traits  and  Mental  Age 56 

Table  XV.    Intercorrelations  between  Physical  Traits,  Chron- 
ological  and   Mental   Age 57 

Table   XVI.    Partial   Correlations   between   Physical   Traits, 

Chronological    and    Mental    Age 57 

5.  Summary  and  Conclusions  58 

IV.  GENERAL  CONCLUSIONS   58 

REFERENCES    60 


MENTAL   GROWTH   CURVE   OF  NORMAL 
AND  SUPERIOR  CHILDREN 

I.     THE  MENTAL  GROWTH  CURVE 

1.  Statement  of  the  Problem.  Contemporary  discussions  of 
the  mental  growth  curve  have  their  parallel  in  the  early  history 
of  anthropometry,  when  scientists  attempted  to  find  the  general 
laws  of  growth  and  to  depict  the  trend  of  the  average  curve  of 
physical  development.  Refinement  of  technique  and  a  better 
analysis  of  the  growth  process  have  shown  wide  individual  dif- 
ferences in  the  growth  of  children,  which  make  it  impossible  to 
represent  these  variations  adequately  by  a  single  mean  curve.  It 
is  now  known  that  there  are  differences  in  the  curves  for  boys 
and  girls,  for  tall  and  short  children,  for  physiologically  accel- 
erated and  retarded  children,  as  well  as  for  children  of  different 
race,  different  environment,  and  different  social  status. 

On  the  analogy  of  the  physical  growth  curve  a  number  of 
writers  have  constructed  theoretical  mental  growth  curves,  gen- 
erally with  rather  a  steep  rise  in  the  early  years  of  life  and  a 
flattening  out  after  the  age  of  puberty.  One  author  has  suggested, 
without  experimental  data,  that  this  curve  should  really  be  con- 
cave in  the  early  years,  owning  to  what  he  believes  to  be  the  slow 
rate  of  development  during  infancy.  The  concept  of  different 
rates  of  development  in  the  subnormal  classes  has  become  so 
firmly  established  that  text-books  generally  visualize  for  the 
student  the  supposed  growth  curves  of  the  three  classical  levels 
of  feeblemindedness.  It  has  also  been  suggested  in  the  literature 
that  superior  children  grow  at  a  faster  rate  and  have  a  steeper 
curve  than  the  average. 

All  of  these  problems  concerning  the  general  trend  of  the 
growth  curve,  the  rate  of  improvement  of  children  of  different 
intellectual  ability,  variability  in  mental  development,  the  pos- 
sibility of  prediction  in  mental  growth,  and  the  relation  between 
physical  and  mental  growth  can  be  solved  only  through  a  study 
of  consecutive  re-examinations  and  observations  of  the  same  group 
of  children  throughout  a  number  of  years.  The  data  of  this  study 


6 


IOWA  STUDIES  IN  CHILD  WELFARE 


furnish  the  basis  for  the  beginning  of  an  empirical  determination 
of  these  aspects  of  the  mental  growth  process. 

2.  Data  for  this  Study.  In  September,  1917,  several  hundred 
children  were  examined  at  the  Iowa  Child  Welfare  Research  Sta- 
tion by  the  Stanford  Revision  of  the  Binet  Scale,  with  a  view  to 
following  the  mental  development  of  the  children  from  year  to 
year.1  The  continuity  of  the  work  was  interrupted  by  war  con- 
ditions2 and  by  the  shifting3  of  the  school  population  particularly 
characteristic  of  a  university  town,  but  143  individual  records  are 
sufficiently  complete  for  the  purposes  of  this  analysis.  Chart  I 

CHART  I 

TYPICAL  RECORD  CARD  FOR  SUCCESSIVE   EXAMINA- 
TIONS. 


NAME 


,  K 


DATE  or 


DATE  or  EXAM.-  1 ,1-8-17  £  .i/r  3>  nffjn  4  n/5fco  5 
GRADE 


CHRONOLOGICAL  AGE 


Curing  the  first  year  the  Yerkes-Bridges  Point  Scale  was  given  at  the  same  time 
as  the  Stanford  Revision,  or  a  day  later.  Although  this  study  is  limited  to  the  data 
from  the  Stanford  Revision,  the  Pearson  coefficient  of  correlation  hetween  the  ratings 
by  the  two  scales,  all  of  the  examinations  being  made  by  the  same  individual,  was  found 
to  be  for  76  cases  +.888  with  a  P.E.  of  ±.016. 

*The  original  plan  for  the  re-examinations  had  the  support  of  the  Acting  Director 
of  the  Child  Welfare  Research  Station,  Ellsworth  Faris,  during  the  Director's  absence 
in  military  service. 

8A  number  of  children,  who  had  left  the  university  school  were  followed  up  and 
examined  in  the  public  schools.  A  fifth  examination  on  one  girl  was  obtained  through 
the  courtesy  of  Professor  L.  W.  Cole,  who  examined  her  in  Colorado  Springs. 


MENTAL  GROWTH  CURVE  7 

shows  a  typical  record  for  successive  examinations.  The  records 
may  be  divided  into  four  groups:  (a)  56  having  two  examina- 
tions; (b)  51  additional  cases  having  three  examinations;  (c)  42 
of  the  three  examination  cases  on  whom  a  fourth  examination 
was  obtained;  (d)  additional  36  cases  having  five  consecutive  ex- 
aminations. 

The  conditions  for  a  study  of  this  kind  were  particularly  favor- 
able. The  University  Observational  Schools,  in  the  same  building 
as  the  Child  Welfare  Research  Station,  are  attended  largely  by 
the  children  of  the  professional  and  business  men  of  the  city  and 
of  prosperous  farmers  nearby.  The  tuition  is  small,  making  the 
expense  comparable  to  that  of  children  attending  the  public 
schools  of  the  town  where  text-books  are  not  supplied.  The  tone 
of  the  school  is  free  and  democratic.  The  children  are  accustomed 
to  all  sorts  of  educational  and  psychological  experiments  and  re- 
gard the  annual  re-examination  as  a  regular  part  of  the  school  pro- 
gram. There  is  no  reason  to  believe  that  any  undue  amount  of 
communication  or  discussion  went  on  among  the  children  in  re- 
gard to  the  mental  tests;  in  fact,  the  examiner  frequently  noted 
the  fact  that  a  child  remembered  having  been  asked  a  certain 
question  a  year  ago  but  did  not  give  further  evidence  that  the 
answer  had  been  learned.  The  investigation  had  the  interest  and 
support  of  the  school  staff,  most  of  whom  were  college  graduates 
who  were  anxious  to  make  the  experimental  conditions  as  favor- 
able as  possible. 

The  examinations  were  given  by  four  psychologists1  during  the 
period  between  September,  1917,  and  May,  1921.  In  all  485 
mental  age  determinations  were  made  on  143  children.  Of  these 
178  were  given  by  Miss  Vest,  8  by  Miss  Schriefer  (who  was  de- 
voting her  time  to  the  examination  of  other  children  entering  the 
school),  77  by  Miss  Wagoner,  and  222  by  Miss  Stecher. 

With  a  view  to  tracing  the  possible  effect  of  the  personal  equa- 
tion, the  material  was  arranged  (Table  XI)  so  as  to  show  what 
proportion  of  the  children  in  a  given  group  were  examined  by 
the  same  examiner.2  In  the  Five  Examination  Group  both  the 
first  and  second  examinations  were  made  by  Miss  Vest  in  91.4% 
of  the  cases;  in  the  Four  Examination  Group  Miss  Vest  gave  30.2% 
of  the  repeated  examinations,  in  the  Three  Examination  Group 


1Eloise  Vest,  A.  M.,  Louise  Schriefer,  A.  M.,  Lovisa  Wagoner,  A.  M.,  Lorle  I.  Stecher, 
Ph.  D. 

In  the  statistical  treatment  of  the  data  in  this  study  the  writers  had  the  co-operation 
of  Gladys  M.  Fairbanks,  A.  M. 


8  IOWA  STUDIES  IN  CHILD  WELFARE 

22.2%,  and  in  the  Two  Examination  Group  28.6%.  Consecutive 
examinations  of  the  same  children  were  given  by  Miss  Stecher 
as  follows:  in  the  Two  Examination  Group  3.5%  of  the  first  and 
second;  in  the  Four  Examination  Group  18.6%  of  the  second  and 
third,  18.6%  of  the  second  and  fourth,  100%  of  the  third  and 
fourth;  in  the  Five  Examination  Group  40%  of  the  third  and 
fourth,  40%  of  the  third  and  fifth,  100%  of  the  fourth  and  fifth. 
That  re-examination  by  the  same  person  is  of  practically  no  sig- 
nificance in  raising  the  correlation  is  shown  in  connection  with  the 
coefficients  of  correlation  on  page  45. 

The  subjects  of  the  study  were  of  average  and  superior  intel- 
ligence with  a  range  of  I.  Q.  from  90  to  167.  The  four  groups 
were  nearly  equal  in  mental  ability  as  shown  by  the  mean  I.  Q. 
of  the  boys  and  girls  of  the  different  groups. 

Group  5  Exam.         4  Exam.  3  Exam.  2  Exam. 

Boys  120.6  114.0  112.8  115.0 

Girls  118.8  113.6  112.3  113.4 

It  will  be  noted  that  the  mental  ability  of  the  boys  was  prac- 
tically the  same  as  that  of  the  girls. 

3.  Method  of  Determining  the  Mental  Growth  Curve.  Terman 
(26)  1919,  p.  127,  has  stated  that  "the  standardization  of  the 
Binet  scale  on  the  basis  of  age  norms  makes  it  a  valuable  instru- 
ment for  the  investigation  of  mental  growth  curves."  The  mental 
growth  curves  presented  herewith  are  probably  the  first  curves 
for  superior  and  average  children  of  the  development  of  general 
intelligence  studied  by  means  of  repeated  examinations  on  the 
same  children. 

The  mental  examinations  on  which  these  growth  curves  are  based 
were  made  at  irregular  intervals,  ranging  on  the  average  from 
6  to  16  months  within  the  period  of  four  years.  In  order  to  plot 
the  curve  at  the  customary  one-year  intervals,  the  mental  ages, 
instead  of  being  assigned  to  the  year  nearest  the  chronological 
age,  as  is  the  usual  custom,  were  calculated  and  weighted  in  such 
a  manner  as  to  give  the  mental  age  at  exact  years.  This  method 
assumes  that  the  child  continues  to  grow  mentally  at  the  same 
rate  between  the  examination  intervals.  A  child  actually  meas- 
ured at  the  age  of  5  years-5  months  would,  under  the  usual 
method,  be  considered  as  five  years  and  its  mental  age  averaged 
with  the  mental  age  of  other  children  who  might  actually  have 
varied  between  4  years-7  months  and  5  years-6  months  at  the  time 
of  the  examination.  To  prevent  this  distortion  of  the  real  age, 


MENTAL  GROWTH  CURVE  9 

mental  and  chronological,  a  new  mental  age  was  computed  for 
each  chronological  age  during  the  period  of  measurement.  The 
method  used  was  as  follows : 

For  each  child  the  difference  between  every  two  successive 
chronological  ages  and  every  two  successive  mental  ages  was  cal- 
culated and  the  rate  of  improvement  obtained  by  dividing  the 
difference  in  mental  age  by  the  difference  in  chronological  age. 
For  example,  take  the  case  of  a  boy  who  had  his  second  examina- 
tion at  the  age  of  6  years-1  month,  and  his  third  examination  at 
the  age  of  7  years-2  months,  giving  a  difference  in  chronological 
age  of  13  months.  His  mental  age  at  the  earlier  examination  was 
8  years-8  months,  and  at  the  later,  10  years-2  months,  the  differ- 
ence in  mental  age  being  18  mental  months.  The  mental  age 
difference  divided  by  the  chronological  age  difference  results  in 
a  rate  of  improvement  of  1.38.  This  means  that  he  grew  1.38 
mental  months  for  every  month  of  chronological  age.  The  mental 
age  at  the  time  of  the  earlier  examination  was  then  corrected  by 
subtracting  from  the  mental  age  of  8  years-8  months,  or  104 
mental  months,  the  number  of  mental  months  equivalent  to  one 
month's  growth  at  the  rate  of  1.33  (which  is  the  rate  at  which 
he  was  growing  previous  to  6-1).  This  gives  a  new  mental  age 
at  6  years  of  104  mental  months — 1.33  mental  months,  or  102.67 
mental  months.  The  corrected  mental  age  at  6  years  was  102.67 
months.  The  corrected  mental  age  at  7  will  be  the  mental  age 
at  6  years-1  month,  -f-11  months  at  the  rate  of  1.38,  or  102.67-f- 
(11X1.38)  or  117.85  mental  months. 

The  resultant  mental  ages  were  averaged  for  each  chronological 
age  from  5  to  14  for  all  of  the  boys  and  all  of  the  girls  of  the 
group  and  for  the  normal  and  superior  boys  and  girls  separately. 
The  resultant  mental  growth  curve  is  shown  in  Table  I  and 
Chart  II. 

The  rates  of  growth  used  for  correcting  the  mental  ages  from 
the  exact  year  to  year  by  the  method  of  monthly  rates  described 
above  were  averaged  by  chronological  age  groups  to  give  the 
total  growth  of  each  child  for  all  year  intervals.  The  resultant 
composite  rates  were  averaged  for  each  year  interval  to  obtain 
the  annual  rate  of  growth.  The  corrected  mental  ages  were  then 
divided  by  the  chronological  ages  at  the  exact  years  in  order  to 
determine  the  new  rate  of  improvement  between  every  two  suc- 
cessive mental  ages.  These  new  rates  were  averaged  by  years  to 
give  the  rate  of  mental  growth  shown  in  Table  III  and  Chart  V. 


10 


IOWA  STUDIES  IN  CHILD  WELFARE 


The  new  I.  Q.'s  for  each  exact  chronological  age  were  averaged 
to  give  Chart  IV  and  Table  II. 

4.  The  Analysis  of  the  Mental  Growth  Curve.  The  mental 
growth  curves  obtained  by  the  individualizing  method  from  con- 
secutive measurements  of  superior  and  average  boys  and  girls  be- 
tween the  ages  5  to  14  present  at  first  glance  the  appearance  of 
a  straight  line.  The  familiar  parabolic  character  of  the  theoret- 
ical growth  curve  is  lacking,  since  our  data  furnish  us  no  de- 
terminations for  ages  14  to  16,  during  which  this  slowing  up  of 
mental  growth  is  supposed  to  take  place. 


TABLE  I 

MEAN  MENTAL  AGE  IN  MONTHS  OF  SUPERIOR  AND  AVERAGE  BOYS  AND 

GIRLS  FOR  SUCCESSIVE  CHRONOLOGICAL  AGES 

(Based  on  487  Consecutive  Examinations) 

Boys 

Girls 

Intelligence 

Intelligence 

Intelligence 

Intelligence 

Chronological 

Quotient 

Quotient 

Quotient 

Quotient 

Age 

110+ 

90-110 

110+ 

90-110 

(Superior) 

(Average) 

(Superior) 

(Average) 

5 

70.6 

60.7 

72.0 

62.5 

6 

88.7 

75.6 

85.0 

73.9 

7 

102.2 

87.4 

102.2 

88.9 

8 

118.7 

100.4 

116.3 

100.9 

9 

131.4 

109.2 

131.1 

112.9 

10 

144.0 

117.7 

145.5 

122.4 

11 

160.5 

130.5 

158.5 

133.3 

12 

181.0 

143.1 

184.1 

141.5 

13 

190.0 

157.2 

196.0 

166.5 

14 

208.9 

168.0 

201.0 

182.9 

It  is  apparent  from  these  curves  that  superior  and  average  chil- 
dren develop  at  different  levels  and  that  children  of  these  dif- 
ferent intellectual  levels  grow  increasingly  dissimilar  with  in- 
crease in  chronological  age.  For  example,  at  the  age  of  5  the 
superior  and  average  boys  have  a  mental  age  of  71  and  61  mental 
months  respectively,  but  at  14  the  superior  have  209  and  the  aver- 
age 168.  The  difference  of  10  points  at  5  years  has  increased  to 
41  points  at  14  years.  The  girls  show  similar  differences. 

This  divergence  in  the  growth  curves  of  average  and  superior 
children  has  long  been  assumed  as  probable  but  has  not  heretofore 
been  empirically  demonstrated.  The  concept  of  the  I.  Q.  pre- 


220 


MENTAL  GROWTH  CURVE 
CHART  II 


11 


GROWTH   CURVES  FOP 
SUPERIOR  AND  AVERAGE  CHILDREN 


/        5       6        7       a       9       IO      II      IZ 

Qhronological  Age   in    Yeor9 

supposes  a  certain  divergence  in  the  curves  of  the  superior  and 
the  average  child,  as  the  superior  child  has  to  grow  at  a  rate 
greater  than  one  mental  month  for  one  chronological  month  in 
order  to  maintain  a  constant  I.  Q. 


12  IOWA  STUDIES  IN  CHILD  WELFARE 

The  general  straight  line  appearance  previously  noted  is  espe- 
cially apparent  in  the  growth  curve  for  boys.  Further  analysis 
reveals,  however,  a  very  significant  change  in  the  trend  with  the 
approach  of  adolescence.  This  is  especially  marked  in  the  curve 
for  girls  where  there  is  a  rise  in  mental  development  in  the  supe- 
rior girls  between  the  ages  11  to  12  and  in  the  average  girls  a  year 
later,  between  the  ages  12  to  13.  The  superior  boys  show  a  similar 
acceleration  in  mental  growth  at  about  12 — somewhat  later  than 
in  the  case  of  the  superior  girls.  The  boys  of  average  mental 
ability  have  not  yet  shown  this  acceleration  up  to  14  years,  which 
is  the  latest  age  for  which  we  have  a  sufficient  number  of  cases. 
It  seems  unlikely  that  this  rise  in  the  curve  of  mental  growth  can 
be  explained  by  defects  in  the  measuring  scale  at  the  adolescent 
ages.  There  is  no  reason  to  believe  that  the  scale  was  not  equally 
well  standardized  at  all  ages.  The  increased  incline  of  the  curve 
extends,  moreover,  through  several  ages,  and  it  is  not  probable 
that  the  tests  would  be  too  easy  throughout  these  years. 

The  mental  growth  curves  of  the  boys  and  girls  cross  repeat- 
edly. There  is,  however,  a  tendency  in  the  earlier  ages  for  the 
average  girls  to  be  a  little  higher  in  mental  age  than  the  average 
boys,  in  the  later  ages  for  the  girls  of  both  groups  to  be  a  little 
superior  to  the  boys.  While  not  without  exception,  this  adoles- 
cent superiority  of  girls  is  in  accordance  with  other  facts  indica- 
tive of  the  earlier  maturity  of  girls. 

There  has  been  in  recent  years  a  movement  to  discredit  charac- 
teristic changes  in  intellectual  traits  as  a  result  of  adolescence. 
This  point  of  view,  which  is  probably  a  reaction  to  undue  senti- 
mental emphasis  of  those  changes  current  in  the  psychology  of 
twenty  years  ago,  is  expressed  by  Terman  (25)  1917,  p.  60,  who 
maintains  there  is  little  evidence  of  periodicity,  or  irregularity 
as  far  as  general  intelligence  is  concerned,  and  throws  doubt  on  the 
existence  of  the  adolescent  spurt.  Although  there  is  obviously  no 
time  in  the  mental  development  of  the  child  when  new  mental 
traits  suddenly  appear,  the  rise  in  the  mental  growth  curves  ap- 
parent at  the  ages  of  11  to  14  may  be  attributed  to  increased 
strength  of  traits  that  have  long  been  developing,  or  to  increased 
mental  vigor  similar  to  the  accelerated  growth  in  physical  traits. 

The  existence  of  such  a  period  of  increased  vigor  would  not 
necessarily  interfere  with  the  stability  of  the  I.  Q.,  providing  the 
scale  was  adapted  in  difficulty  to  such  a  change.  It  certainly 
would  not  affect  the  individual's  position  in  the  group  relative 


MENTAL  GROWTH  CURVE 
CHART  III 


13 


tao 

709 

tro 

669 

(0    160 
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I/O 

433 

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GROW  T 

//   CURVES 
HEIGHT 

(Baldwin) 
2  -Short 

vidual  Curves, 

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S          6           7         S          9          10         li          12         13         A*         IS         '6         ir        It 
Aye    >n   Y€or* 

to  a  norm,  since  the  norm  at  these  ages  would  also  be  higher  if 
all  children  developed  in  a  similar  way.  A  child 's  physical  status 
in  height,  for  example,  remains  relatively  constant  with  reference 
to  its  group  from  age  6  through  adolescence,  as  shown  by  Baldwin 
(1)  1914,  though  the  norms  and  individual  curves  may  show 
adolescent  accelerations. 

The  mental  growth  curves  are  strikingly  similar  to  the  physical 
growth  curves  in  height  as  shown  in  Chart  III.  This  chart  here 
published  for  the  first  time  illustrates  the  differences  in  the 
growth  of  tall,  average  and  short  girls  and  of  a  tall  and  a  short 


14 


IOWA  STUDIES  IN  CHILD  WELFARE 


boy  as  compared  with  the  norms  for  boys  and  girls.  The  norms 
for  average  boys  and  girls  are  based  on  6  to  10  years  of  semi- 
annual measurements  for  60  boys  and  60  girls.  The  curves  for 
tall  girls  are  based  on  similar  material  for  52  cases  distributed 
above  the  norm,  and  the  curves  for  short  girls  on  28  cases  con- 
siderably below  the  norm.  The  curves  show  the  same  phenomena 
that  have  been  pointed  out  in  connection  with  the  mental  growth 
curves.  In  both  cases  the  curve  at  the  higher  level  shows  the 
acceleration  at  an  earlier  age. 


TABLE  II 
MEAN   INTELLIGENCE   QUOTIENTS   OF   SUPERIOR   AND   AVERAGE  BOYS  AND 
GIRLS  FOR  SUCCESSIVE  CHRONOLOGICAL  AGES 

Chronological 
Age 

Boys 

Girls 

Intelligence 
Quotient 
110+ 
Superior 

Intelligence 
Quotient 
90-110 
Average 

Intelligence 
Quotient 
110+ 
Superior 

Intelligence 
Quotient 
90-110 
Average 

5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

117.6 
123.3 
121.6 
123.6 
121.7 
119.9 
121.5 
125.7 
121.5 
124.3 

101.2 
105.0 
104.0 
104.6 
101.1 
98.1 
98.8 
99.4 
100.8 
100.0 

119.9 
118.0 
121.7 
121.1 
120.5 
120.3 
119.8 
127.9 
125.7 
119.7 

104.1 
102.6 
105.9 
105.1 
lt)4.6 
102.1 
99.9 
98.2 
106.7 
108.9 

5.  The  Analysis  of  the  I.  Q.  Curve.  The  mean  intelligence 
quotients  (Table  II)  and  the  I.  Q.  curves  (Chart  IV)  for  superior 
and  average  boys  and  girls  show  some  of  the  same  characteristics 
observed  in  the  mental  growth  curves.  The  curves  are  in  general 
approximately  horizontal,  confirming  within  limitations  the  con- 
stancy of  the  I.  Q.  There  appear  to  be,  however,  certain  definite 
phenomena  associated  with  physiological  development  that  show 
themselves  in  a  decrease  or  increase  in  the  I.  Q.  at  certain  chrono- 
logical ages.  A  study  of  the  physical  development  of  young  chil- 
dren shows  that  there  is  considerable  fluctuation  between  the 
ages  4  and  7.  These  I.  Q.  curves  suggest  a  similar  condition  with 
a  small  spurt  in  mental  development,  appearing  a  little  later  in 
the  boys  than  in  the  girls.  Both  superior  boys  and  girls  show 
a  rise  in  the  I.  Q.  between  the  ages  of  11  and  12.  Average  girls 


MENTAL  GROWTH  CURVE 


15 


CHART  IV 


160 
ISO 
140 
ISO 


I.  Q.    CURVES 
or 

SUPERIOR  AND  AVERAGE   CHILDREN 

SUP 'f* 'to*  ^— ^—       Bars 

AvtKAtl     —  —  —•  SlAlf 


a       9 

Age  in   Yeora 


10 


II 


12. 


also  show  this  adolescent  acceleration,  although  it  appears  a  year 
later  than  in  the  case  of  superior  girls.  The  I.  Q.  curve  and  the 
mental  growth  curve  of  the  average  boys  do  not  show  this  phe- 
nomenon, possibly  because  they  have  not  reached  this  stage  of 
acceleration. 

6.  Tine  Analysis  of  the  Curve  of  the  Rate  of  Mental  Growth. 
Our  tables  of  original  data  do  not  include  calculations  of  the 
actual  number  of  mental  months  growth  for  one  chronological 
month  between  examinations,  although  these  were  used  in  all 


TABLE  III 
MEAN  RATE  OF  MENTAL  GROWTH  OF  SUPERIOR  AND  AVERAGE  BOYS  AND 
GIKLS  FOR  CHRONOLOGICAL  AGE  INTERVALS 

Chronological 
Age 
Intervals 

Boys 

Girls 

Intelligence 
Quotient 
110+ 
Superior 

Intelligence 
Quotient 
90-110 
Average 

Intelligence 
Quotient 
110+ 
Superior 

Intelligence 
Quotient 
90-110 
Average 

5-6 
6-7 
7-8 
8-9 
9-10 
1<K11 
11-12 
12-13 
13-14 

1.5 

1.2 
1.5 
1.4 
1.4 
1.8 
1.8 
(1.1) 
1.5 

1.0 
1.1 
1.2 
1.3 
1.0 
1.1 
1.3 
1.3 
1.1 

1.2 
1.5 
1.2 
1.3 
1.5 
L6 
2.2 
1.9 
1.9 

.8 
1.1 
1.1 
1.2 
.8 
1.1 
1.1 
1.6 
1.4 

16 


IOWA  STUDIES  IN  CHILD  WELFAKE 


cases  as  a  basis  for  the  curve  of  the  rate  of  mental  growth.  In- 
spection of  the  tables  will  show  for  individual  children  great 
fluctuation  in  the  rate  from  examination  to  examination.  A  child 
whose  rate  from  the  first  to  the  second  examination  is  1.56  mental 
months  for  each  month  of  chronological  age  may  show  between 
the  second  and  third  examination  a  rate  of  .23  mental  months 
for  each  chronological  month.  Part  of  this  discrepancy  is  of 
course  due  to  the  experimental  error  of  each  single  mental  age 
determination,  but  the  size  of  many  of  the  irregularities  cannot 
be  explained  on  this  basis.  It  appears  that  there  is  no  rate  of 
improvement  which  is  characteristic  of  the  individual  and  uni- 
formly maintained  throughout  his  years  of  mental  growth  al- 
though an  approximately  constant  rate  is  maintained  in  many 
cases. 

Table  III  and  Chart  V  show  the  mean  rate  of  mental  growth 
for  these  children.     The  average  children  grow  approximately 


CHART  V 


Cnronolag/cot    Agt    interval* 


•»  •«  <J 


one  mental  month  for  each  chronological  month,  while  the  supe- 
rior children  have  a  higher  rate  (shown  by  the  curve  at  a  higher 
level)  except  in  the  case  of  boys  between  12  and  13,  where  the 
small  number  of  cases  results  in  a  decreased  rate  (printed  in 
parenthesis  in  Table  III  and  represented  by  a  dotted  line  in  Chart 
V).  The  effect  may  also  be  noted  in  the  mental  growth  curve 
for  superior  boys,  Chart  I. 

There  is  little  difference,  on  the  average,  in  the  rate  of  growth 
of  these  two  groups  of  children.     In  no  case  is  the  difference 


MENTAL  GROWTH  CURVE  17 

greater  than  seven-tenths  of  a  year.  These  figures  cannot  of 
course  be  considered  as  norms,  since  they  depend  upon  the  selec- 
tion of  cases  included  in  the  study.  The  addition  of  more  cases  of 
very  superior  intelligence,  or  of  more  cases  of  I.  Q.'s  below  100 
would  have  increased  the  difference. 

The  general  prepubertal  increase  in  mental  development  be- 
comes, evident  earlier  in  the  case  of  superior  children  than  in 
average  children,  and  in  the  case  of  superior  girls  about  a  year 
earlier  than  in  average  boys.  In  comparing  the  curves  it  should 
be  kept  in  mind  that  a  child  who  has  been  growing  at  a  certain 
rate  and  then  reaches  a  period  of  little  or  no  increase  will  have 
to  reattain  the  rate  of  growth  at  which  he  was  previously  de- 
veloping before  an  actual  acceleration  in  growth  can  be  consid- 
ered as  taking  place.  The  period  of  acceleration  is  therefore  later 
than  the  point  in  the  curve  at  which  the  steep  rise  begins.  In 
general  all  of  these  curves  show  less  difference  between  average 
and  superior  boys  in  regard  to  these  adolescent  phenomena  than 
between  average  and  superior  girls,  who  are  usually  a  year  apart 
in  their  general  development. 

Our  data  do  not  permit  us  to  give  a  definite  answer  to  the  ques- 
tion whether  superior  children  grow  more  superior  as  time  goes 
on  through  an  increase  in  the  rate  of  mental  growth.  The  curves 
for  the  two  groups  of  children  seem  to  diverge  slightly  at  the 
higher  ages,  especially  in  the  case  of  girls  at  the  adolescent  years. 
The  facts  in  regard  to  the  change  of  I.  Q.  to  be  reported  later  on 
page  . .  seem  also  to  indicate  some  characteristic  differences  in 
the  growth  of  children  of  different  I.  Q.  level.  We  should  hesi- 
tate, however,  to  make  any  generalization  in  regard  to  this  matter 
from  the  material  presented  in  this  study. 

7.  Mean  Group  Differences  at  Successive  Examinations.  Table 
V  is  purely  descriptive,  presenting  the  mean  chronological  age 
at  successive  examinations  and  the  mean  interval  between  exam- 
inations for  use  in  interpreting  the  findings  in  other  tables.  The 
findings  of  Table  IV  are  averages  of  the  I.  Q.'s  obtained  at  each 
examination  by  the  children  of  each  particular  group. 

It  is  a  very  significant  fact  that  the  mean  I.  Q.  of  each  of  the 
four  groups  of  children  increased  with  each  successive  examina- 
tion, which  must  be  regarded  as  an  effect  of  greater  habituation 
or  practice.  The  increase  in  the  mean  I.  Q.  is  proportionate  to 
the  number  of  re-examinations. 


18 


IOWA  STUDIES  IN  CHILD  WELFARE 


The  mean  I.  Q.  for  the  Five  Examination  Group  increased  from 
115.39  through  119.5,  119.75  and  123.91  to  126.7.  The  mean  I.  Q. 
for  the  Four  Examination  Group  increased  from  111.06  through 

112.02  and  115.16  to  118.20.    The  mean  I.  Q.  for  the  Three  Ex- 
amination Group  increased  from  110.59  through  111.80  to  115.21. 
The  mean  I.  Q.  for  the  Two  Examination  Group  increased  from 

112.3  to  115.8.    This  increase  in  I.  Q.  has  been  noted  by  previous 
workers  on  a  single  retest  in  the  summary  by  Rugg  and  Coll- 
oton  (21). 


TABLE  IV 
MEAN  INTELLIGENCE  QUOTIENTS  AT  SUCCESSIVE  EXAMINATIONS 

Group 

No.  of 
Cases 

Exam.  1 

Exam.  2 

Exam.  3 

Exam.  4 

Exam.  5 

5 
4 
3 
2 

36 
42 
51 

56 

115.4 
111.1 
110.6 
112.3 

119.5 
112.0 
111.8 
115.8 

119.8 
115.2 
115.2 

123.9 
118.2 

126.7 



There  is  also  an  increase  in  the  mean  rate  of  improvement  upon 
successive  examinations.  To  investigate  this  phase  of  the  practice 
effect,  the  data  for  the  Four  and  the  Five  Examination  Groups 
were  worked  over  to  give  for  each  child  the  amount  of  increase 
in  mental  age  months  for  each  month  of  chronological  age  in- 
crease between  the  first  and  second  examination,  the  second  and 
third  and  the  third  and  fourth.  The  means  of  these  individual 
rates  of  improvement  reveal  a  general  increase  in  the  rate  of 
mental  development  which  is  especially  marked  between  the  third 
and  fourth  examination  in  the  case  of  the  girls. 


Examination 

Boys 

Girls 


No.  cases 
37 
34 


I-II 

Eate 
1.48 
1.29 


II-III 
Eate 
1.42 
1.64 


III-IV 
Eate 
1.73 

2.40 


8.  Discussion  and  Literature.  It  is  extremely  probable  that 
the  theoretical  mental  growth  curves  found  in  so  many  text- 
books really  misrepresent  the  facts  of  mental  development.  It 
has  been  the  custom  to  draw  the  growth  curves  of  children  of 
different  degrees  of  ability  as  if  all  of  these  curves  began  with 
zero  ability  at  the  time  of  birth  and  from  that  time  on  rose 
steadily.  From  all  that  we  know  in  regard  to  differences  in  the 
mental  capacity  of  young  children,  the  curves  of  mental  develop- 
ment, like  the  curves  of  physical  development,  begin  at  dif- 


MENTAL  GROWTH  CURVE 


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ferent  levels  (points). 
There  are  individual  men- 
tal differences  at  birth  as 
there  are  individual  dif- 
ferences in  height.  It  is 
not  conceivable  that  the 
feebleminded  child  should 
begin  at  the  same  point 
with  the  child  of  average 
or  superior  ability  and 
then  drop  back  in  the  race 
as  his  more  gifted  brothers 
gain.  The  truth  of  the 
matter  is,  he  runs  on  a 
relatively  lower  level 
throughout  life. 

Much  of  the  work  on 
retests  of  children  has 
been  done  with  feeble- 
minded subjects.  While  it 
is  impossible  in  this  study 
on  normal  and  superior 
children  to  go  into  the 
question  of  growth  curves 
of  the  feebleminded,  it 
will  orientate  the  problem 
if  we  review  briefly  such 
other  studies  as  have  been 
made  with  repeated  exam- 
inations. Bobertag  (6)  p. 
528,  reported  in  1912  as  a 
result  of  retests  on  83 
children  whom  he  had  ex- 
amined the  year  before 
that  children  whose  intel- 
ligence is  above  average 
advance  more  rapidly ; 
those  whose  intelligence  is 
below  average  advance 
more  slowly.  He  main- 
tained (p.  531)  that  if  one 


20  IOWA  STUDIES  IN  CHILD  WELFARE 

limits  one's  self  to  a  few  successive  years — 8,  9,  10,  for  example — 
one  could  say  that  the  I.  Q.  is  approximately  constant.  If,  how- 
ever, one  considers  all  the  ages,  or  the  whole  developmental  course 
of  children's  intelligence  it  is  very  questionable  whether  the  as- 
sumption of  a  constant  I.  Q.  is  tenable. 

Berry  (4)  in  1913  found  on  a  retest  of  82  children  that  the 
normal  subjects  made  an  average  gain  of  1  year,  and  the  feeble- 
minded— mental  ages  4-11  years — an  average  gain  of  .5  of  a  year. 
He  did  not  report  the  correlation  between  the  examinations. 

Bloch  (5)  1915  re-examined  defective  children  by  the  Binet 
scale. 

Stern  (23)  (24)  1914  and  1916,  who  discussed  the  subject  at 
length,  but  without  experimental  data  of  his  own,  believed  that 
the  I.  Q.  did  not  afford  an  actually  constant  expression  of  degree 
of  feeblemindedness  but  showed  a  tendency  to  fall  in  value  as 
chronological  age  increased  and  the  age  of  arrest  was  approached. 

Descoeudres  (9)  1915  retested  26  children  of  a  special  class 
and  found  the  I.  Q.  very  similar  to  the  previous  one  with  a  greater 
tendency  to  increase.  Cases  with  three  or  four  examinations 
showed  practically  the  same  I.  Q.  with  less  than  50%  variation. 

Terman  (25)  p.  55,  1917  concluded  from  re-examinations  that 
"the  results  of  140  such  tests  show  as  far  as  the  age  of  13  or  14, 
even  when  the  tests  are  separated  by  as  much  as  five  years, 
changes  of  10  points  in  12  are  relatively  rare.  In  general,  it  can 
be  said  that  the  superior  children  of  the  first  test  are  found  supe- 
rior in  the  second,  the  average  remained  average,  the  inferior 
remain  inferior,  the  feebleminded  remain  feebleminded  and  nearly 
always  in  approximately  the  same  degree.  The  most  marked  ex- 
ceptions to  this  rule  are  found  with  the  feebleminded  whose  in- 
telligence quotient  shows  a  tendency  to  decrease  considerably. ' ' 

Cuneo  and  Terman  (8)  1918,  retested  77  children  and  found 
high  correlations  between  the  two  tests. 

Terman  (26)  1919  found  considerable  agreement  in  the  I.  Q.'s 
of  46  children  tested  three  or  more  times.  He  says,  p.  147:  "It 
is  possible  that  feebleminded  children  testing  below  60  are  less 
likely  to  hold  their  own  than  those  of  milder  degree  of  defect. 
.  .  .  On  the  other  hand  the  I.  Q.  as  determined  by  the  Stanford- 
Binet  (or  any  other  intelligence  scale  yet  devised)  cannot  indef- 
initely hold  its  constancy  in  the  case  of  children  who  are  excep- 
tionally superior." 


MENTAL  GROWTH  CURVE  21 

Wallin  (28)  1919  discussed  the  use  of  the  I.  Q.  in  classification 
without  data  from  retests.  His  article  has  been  critically  re- 
viewed by  Rosenow  (20)  1920,  who  presents  experimental  evi- 
dence of  approximate  stability  of  the  I.  Q.  from  retests  of  69 
cases  examined  at  about  10  months  interval. 

Wallin  (29)  1921  reported  re-examinations  on  153  children  by 
different  revisions  of  the  Binet  tests. 

Kuhlmann  (17)  (18)  who  had  discussed  the  intelligence  of  the 
feeble-minded  is  also  reported  by  Hollingworth  (15)  p.  105  in  1920 
to  have  found  that ' '  On  the  whole  the  I.  Q.  for  a  given  case  remains 
constant  with  a  slight  tendency  on  the  average  to  decrease  after 
the  ages  of  about  nine  or  ten. ' ' 

Kuhlmann  (18a)  1921  reported  results  on  639  cases  ranging  from 
idiocy  to  nearly  normal  mentality  examined  2  to  5  times  within  a 
10  year  period  by  the  Binet  and  Kuhlmann  series.  He  found  that 
the  I.  Q.  decreased  with  age  and  more  for  the  higher  than  for  the 
lower  grades. 

Garrison  (13)  1921  retested  by  the  Stanford-Binet  94  children 
who  had  previously  been  tested  by  the  Goddard  Revision  and 
found  on  the  whole,  a  rather  close  correspondence. 

Doll  (10)  1921,  from  a  study  of  numerous  growth  curves  for 
feebleminded  subjects  who  had  received  at  least  5  annual  exam- 
inations, believes  in  an  age  of  arrest  for  the  feebleminded  beyond 
which  the  I.  Q.  would  decrease.  Terman  (27)  1921  criticizes  this 
presentation  and  the  conclusion  drawn  from  the  data. 

Freeman  (12)  1921,  published  an  important  discussion  on  the 
concept  of  the  I.  Q.  with  reference  to  age  scales  and  point  scales. 

Rugg  and  Colloton  (21)  1921,  have  assembled  the  reports  of 
other  workers  with  Stanford-Binet  tests  and  added  data  from  137 
cases  of  their  own.  They  find  that  with  one  exception  investiga- 
tors have  found  an  average  difference  in  I.  Q.  on  re-examination  of 
4.5  points,  and  confirm  in  some  other  respects  Terman 's  1917  con- 
clusions. 

The  literature  summarized  above  presents  many  interesting 
problems  in  regard  to  the  age  of  arrest  or  the  limit  of  mental 
growth.  Our  data  do  not  extend  far  enough  to  permit  us  to  spec- 
ulate on  the  age  at  which  mental  growth  ceases  in  the  normal  or 
superior  child,  though  there  is  reason  to  suspect  that  the  mental 
age  curves  of  some  of  the  superior  girls  are  beginning  to  flatten 
out  with  a  resulting  decrease  in  I.  Q.  Even  so  this  may  be  merely 


22  IOWA  STUDIES  IN  CHILD  WELFARE 

a  fictitious  slowing  up  of  mental  growth  due  to  the  inevitable 
''bumping"  into  the  upper  limit  of  the  scale. 

SUMMARY  AND  CONCLUSIONS 

1.  The  fundamental  problems  concerning  the  general  trend  of 
the  growth  curve,  the  rate  of  improvement  of  children  of  different 
intellectual  ability,  variability  in  mental  development,  the  pos- 
sibility of  prediction  in  mental  growth  and  the  relation  between 
physical  and  mental  growth  can  be  solved  only  through  a  study 
of  consecutive  reexaminations  and  observations  of  the  same  group 
of  children  throughout  a  number  of  years. 

2.  The  mental  growth  curves  presented  herewith  are  probably 
the  first  curves  for  superior  and  average  children  of  the  develop- 
ment of  general  intelligence  studied  by  means  of  repeated  exam- 
inations on  the  same  children. 

3.  The  curves  constructed  from  the  corrected  mental  age  rat- 
ings do  not  misrepresent  the  actual  growth  process  as  is  the  case 
when  the  chronological  age  is  approximated  to  the  nearest  year. 

4.  It  is  apparent  from  these  curves  that  superior  and  average 
children  develop  at  different  levels  and  that  children  of  these  dif- 
ferent intellectual  levels  grow  increasingly  dissimilar  in  mental 
age  with  increase  in  chronological  age.     This  divergence  in  the 
growth  curves  of  average  and  superior  children  has  long  been 
assumed   as   probable   but   has  not   heretofore    been    empirically 
demonstrated. 

5.  An  analysis  of  the  mental  growth  curve  reveals  a  significant 
change  in  the  trend  with  the  approach  of  adolescence,  which  ap- 
pears earlier  in  the  case  of  superior  children.     There  is  also  an 
adolescent  superiority  of  girls  which  is  in  accordance  with  other 
facts  indicative  of  the  earlier  maturity  of  girls. 

6.  The  mental  growth  curves  are  strikingly  similar  to  the 
physical  growth  curves  in  height. 

7.  The  I.  Q.  curves  are  approximately  horizontal,  confirming 
within  limitations  the  constancy  of  the  I.  Q.    There  are  fluctua- 
tions associated  with  physical  development. 

8.  The  curves  of  the  rate  of  mental  growth  are  higher  for 
superior  than  for  average  children,  and  seem  to  diverge  slightly 
at  the  adolescent  years. 

9.  The  general  prepubertal  increase  appears  earlier  in  the  case 
of  superior  children. 


MENTAL  GROWTH  CURVE  23 

10.  The  mean  I.  Q.  of  each  of  the  four  groups  of  children  in- 
creased with  each  successive  examination,  which  is  probably  an 
effect  of  greater  habituation  or  practice. 

11.  There  is  also  an  increase  in  the  mean  rate  of  improvement 
on  successive  examinations. 

II.    THE  POSSIBILITY  OF  PREDICTION  IN  MENTAL 

GROWTH 

1.  Intelligence  Status  of  Individuals  at  Successive  Examina- 
tions. The  stability  of  the  I.  Q.  is  one  of  the  most  important  prob- 
lems under  discussion  by  psychologists  at  the  present  time.  Upon 
the  relative  stability  of  the  ratio  between  mental  and  chronolog- 
ical age  depends  to  a  large  extent  the  possibility  of  prediction  in 
mental  growth. 

Binet  and  Simon  felt  very  doubtful  of  the  possibility  of  using 
the  I.  Q.  for  prediction.  Even  Bobertag  (5)  and  Stern  (24),  who 
are  among  the  earliest  advocates  of  the  use  of  the  I.  Q.,  did  not 
believe  that  it  would  remain  constant  for  later  ages. 

The  question  of  the  stability  of  the  I.  Q.  has  been  discussed  in 
a  number  of  theoretical  articles.  Some  writers  believe  that  it  re- 
mains practically  constant  and  others  have  found  a  tendency  for 
the  I.  Q.  of  the  feebleminded  to  decrease  and  for  the  I.  Q.  of  the 
superior  to  increase.  Any  conclusive  answer  to  the  question  of 
whether  the  I.  Q.  remains  constant  depends  upon  the  accumula- 
tion of  a  sufficient  number  of  long-time  mental  growth  curves 
for  children  of  different  intellectual  capacity. 

Terman  (26)  1919,  p.  137,  states  the  problem  briefly  thus :  "By 
applying  it  [the  Binet  scale]  repeatedly  to  the  same  children  we 
can  find  out  whether  constancy  or  irregularity  rules.  Prediction 
hinges  on  the  question  whether  a  child  who  is  found  by  the  test 
to  be  a  given  per  cent  above  or  below  the  mental  level  normal 
for  his  age  continues  to  be  accelerated  or  retarded  to  the  same 
degree.  The  answer  is  found  in  the  extent  to  which  the  I.  Q. 
remains  constant." 

Psychologists  who  have  been  accustomed  to  thinking  that  all 
that  was  required  for  a  solution  of  the  problems  of  mental  growth 
was  the  accumulation  of  a  sufficient  number  of  re-examinations 
for  long  periods  will  find  that  the  repetition  of  the  intelligence 
scale  brings  up  many  puzzling  new  problems.  A  study  of  the 
original  data,  Tables  VI  and  VII,  shows  just  what  variations  in 


24 


IOWA  STUDIES  IN  CHILD  WELFARE 


TABLE   VI 
ORIGINAL  DATA  ARRANGED  IN   ORDER  OF  MEAN 

I.  Q.  —  BOYS 

i. 

Average  I.   C 
Examiner 
Chronological 
Terman  Age 
I.    Q  

.    158.0. 
Age   

E.  V. 

5-3 
8-5 
160 

E.  V. 

5-10 
9-1 
156 

2. 

Average  I.   Q.    150.7. 

Examiner    ... 

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  S. 

Chronological 

Age  

5-11 

7-0 

7-11 

8-6 

Terman  Age 

8-5 

9-4 

13-3 

13-9 

I.    Q  

142 

133 

167 

iei 

3. 

Average  I.   Q 

.    143.6. 

Examiner    ... 

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  8. 

Chronological 

Age  

5-1 

6-1 

7-2 

8-1 

8-7 

Terman  Age 

7-4 

8-8 

10-2 

11-7 

12-S 

I.    Q  

144 

142 

142 

143 

147 

4. 

Average  I.  Q 

142.6. 

Examiner    ... 

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S. 

»-•> 

9-3 

10-3 

11  2 

11-8 

Terman  Age 

11-1 

12-1 

15 

16-11 

17-8 

I.    Q.    -  

135 

130 

146 

151 

151 

5. 

Average  I.    Q 

.    138.2. 

Examiner    — 

E.  V. 

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological 

Age   

5-a 

6-9 

7-9 

8-8 

9-2 

Terman  Age 

7-« 

9-9 

10-3 

11-7 

13-0 

I.    Q  

132 

144 

132 

133 

150 

6. 

Average  I.    Q 

.    137. 

Examiner    

L.  W. 

L.  I.  8. 

Chronological 

Age   _ 

5-9 

8-11 

Terman  Age 

7-8 

9-9 

I.   Q  

133 

141 

7. 

Average  I.   Q 

.    134.5. 

Examiner    ... 

E.  V. 

L.  W. 

Chronological 

Age   

6-10 

9-2 

Terman  Age 

8-9 

12-11 

I.    Q  

128 

141 

8. 

Average  I.   Q 

.    131.8. 

Examiner    — 

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  8. 

Chronological 

Age  

10-7 

12-1 

12-7 

13-7 

14-0 

Terman  Age 

12-6 

18-8 

17-2 

18-1 

19-0 

I.    Q  - 

117 

136 

137 

133 

136 

9. 

Average  I.    Q 

.    129.0. 

Examiner    _„ 

L.  W. 

L.  I.  8. 

Chronological 

Age   

9-1 

7-0 

Terman  Age 

7-4 

9-7 

I.   Q  — 

121 

137 

10. 

Average  I.    Q 

.    128.0. 

Examiner    ___ 

E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  S. 

Chronological 

Age 

6-3 

7-4 

9-4 

9-10 

Terman    Age 

8-0 

9-4 

11-4 

13-4 

I.    Q  

128 

127 

121 

136 

11. 

Average  I.   Q 

.    128.0. 

Examiner    .„ 

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

L.  I.  8. 

Chronological 

Age  

6-1 

7-1 

8-8 

9-1 

9-7 

Terman  Age 

7-6 

9-2 

11-3 

11-6 

12-9 

I.    Q.    

123 

129 

129 

126 

133 

12. 

Average  I.   Q 

.    127.6. 

Examiner    ... 

E.  V. 

L.  8. 

L.  I.  8. 

L.  I.  8. 

L.  I.  8. 

Chronological 

Age  

10-6 

12-0 

13-1 

13-6 

14-0 

Terman  Age  . 

12-8 

15-5 

17-0 

17-8 

18-6 

I.    Q  

120 

128 

129 

129 

132 

13. 

Average  I.   Q 

.    127.2. 

Examiner    — 

E.  V. 

L.  I.  8. 

L.  I.  8. 

L.  I.  S. 

Chronological 

Age  

7-1 

8-8 

9-1 

9-6 

Terman  Age 

8-0 

11-2 

12-1 

12-4 

I.    Q  

120 

129 

133 

127 

14. 

Average  I.   Q 

.    126.0. 

Examiner    

L.  W. 

L.  I.  S. 

Chronological 

Age  

7-3 

8-1 

Terman  Age  . 

9-2 

10-2 

I.   Q  

126 

126 

MENTAL  GROWTH  CURVE 


25 


TABLE  VI  —  CONTINUED 
ORIGINAL  DATA  ARRANGED  IN  ORDER  OF  MEAN  I. 

Q.  —  BOYS 

15. 

Average  I.    Q.   124.5. 

Examiner    _ 

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  S. 

Chronological  Age  

9-1 

10-5 

11-0 

11-7 

Terman  Age  _  _ 

10-8 

12-6 

14-6 

14-11 

I.   Q.    -—  -  

117 

120 

132 

129 

18. 

Average  I.    Q.    124.2. 

Examiner    

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological  Age  

8-4 

10-4 

11-3 

11-10 

Terman  Age  -  

10-9 

11-10 

14-1 

15-4 

I.    Q  -  

129 

114 

125 

129 

17. 

Average  I.    Q.   124.0. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological  Age  

8-3 

9-6 

io-e 

11-2 

11-8 

10-1 

11  11 

13-1 

13—11 

14-7 

I.    Q  -  

122 

125 

124 

124 

125 

18. 

Average  I.    Q.   123.5. 

Examiner    

L.  W. 

L.  I.  S. 

Chronological  Age   —  

6-11 

7-10 

Terman  Age  

8-8 

9-7 

I.    Q  -  

125 

122 

19. 

Average  I.   Q.   123.5. 

Examiner    

L.  W. 

L.  I.  S. 

Chronological  Age  

8-7 

9-3 

Terman  Age  

10-4 

11-9 

I.    Q  

120 

127 

20. 

Average  I.    Q.   123.0. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological  Age   

10-4 

11-11 

12-11 

13-6 

13-10 

Terman  Age  

12-8 

15-0 

15-5 

16-3 

16-8 

I.    Q.    

122 

125 

119 

121 

128 

21. 

Average  I.  Q.  122. 

Examiner    

E.  V. 

L.  I.  S. 

Chronological  Age  

5-4 

8-3 

Terman  Age  

0-2 

10-7 

I.   Q  -  

lie 

128 

22. 

Average  I.   Q.   121.7. 

Examiner    

E.  V. 

E.  V. 

L.  I.  S. 

L    I.  S. 

Chronological  Age   

9-8 

11-3 

12-9 

13-3 

Terman  Age  

11-4 

14-1 

15-3 

16-8 

I.    Q  

117 

125 

119 

126 

23. 

Average  I.   Q.    121.2. 

Examiner    

E.  V. 

L.  W. 

L.  I.  S. 

I.  I.  8. 

Chronological  Age   

5-2 

6-6 

7-3 

7-10 

Terman  Age  „ 

5-3 

7-6 

9-5 

10-4 

I-   Q  

109 

115 

129 

132 

24. 

Average  I.   Q.    121.0. 

Examiner    _  

E.  V. 

E.  V. 

Chronological   Age  

10-9 

12-4 

Terman  Age  

11-9 

16-5 

I.    Q  

109 

133 

26. 

Average  I.    Q.   120.8. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L    I.  8. 

L.  I.  8. 

Chronological  Age  

8-6 

9-7 

10-10 

11-7 

12-0 

Terman  Age  

9-11 

11-4 

13-3 

14-4 

14-11 

I.    Q  

lie 

118 

122 

124 

124 

20. 

Average  I.    Q.    120.2. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  8. 

Chronological  Age   

5-1 

5-8 

7-0 

7-8 

8-3 

Terman  Age  

6-10 

7-0 

7-10 

9-6 

10-8 

I.   Q  

114 

123 

111 

124 

129 

27. 

Average  I.   Q.   120.0. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

Chronological  Age  

9-0 

10-0 

11-8 

Terman  Age  —  

10-8 

12-1 

13-0 

I.    Q  

118 

120 

122 

28. 

Average  I.    Q.    120.0. 

Examiner    

L.  W. 

L.  I.  S. 

Chronological   Age   — 

5-9 

M 

Terman  Age  

e-e 

8-2 

I.   Q  

113 

127 

26 


IOWA  STUDIES  IN  CHILD  WELFARE 


TABLE  VI  —  CONTINUED 
ORIGINAL  DATA  ARRANGED  IN  ORDER  OF  MEAN  I. 

Q.  —  BOYS 

29. 

Average   I.    Q.   119.7. 

Examiner    

E.  V. 

E.  V. 

L.  I.  8. 

L    I.  S. 

Chronological  Age  

8-10 

8-4 

9-11 

10-5 

Terman  Age  

7-4 

9-4 

12-0 

14-5 

I.    Q.    

107 

112 

122 

138 

30. 

Average  I.    Q.    119.2. 

Examiner    .  

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S. 

Chronological  Age  ... 

..    .          5-0 

6-« 

7-2 

7-8 

e_  0 

1  11 

8-7 

9-3 

I.    Q.    

115 

122 

119 

121 

31. 

Average  I.   Q.   119.0. 

Examiner    

E.  V. 

E.  V. 

Chronological   Age   — 

7-8 

9-1 

Terman  Age  — 

9-2 

10-6 

I.    Q  

120 

118 

32. 

Average   I.    Q.    118.5. 

Examiner    

E.  V. 

L.  W. 

Chronological   Age  — 

6-0 

7-3 

Terman  Age  —  

6-10 

8-11 

I.    Q  -  

114 

123 

33. 

Average   I.   Q.   118.0. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  8. 

/-(r-                            1               f             |             A 

1  9 

7  1ft 

8-5 

Terman  Age  —  

6-2 

7-0 

8-2 

9-5 

10-1 

I.    Q  

117 

120 

114 

120 

119 

34. 

Average   I.    Q.    118.0. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S. 

Chronological  Age  _._ 

10-1 

11-2 

12-8 

13-2 

13-7 

Terman   Age  

10-4 

12-8 

15-5 

16-6 

17-4 

I.    Q.    

102 

113 

122 

125 

128 

35. 

Average   I.    Q.    117.8. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S 

Chronological  Age  

9-2 

10-3 

11-5 

12-3 

12-8 

Terman  Age  

10-3 

11-11 

14-0 

14-10 

14-10 

I.    Q.    

112 

lift 

122 

121 

117 

36. 

Average   I.    Q.    117.5. 

Examiner    

—  L.S.&E.V. 

L.  I.  S. 

Chronological  Age   

11-8 

14-3 

Terman  Age  

14-3 

16-2 

I.    Q  -  

122 

113 

37. 

Average  I.   Q.   117.5. 

Examiner    

.  E.  V. 

E.  V. 

Chronological   Age  

8-10 

9-11 

Terman   Age    

10-4 

11-9 

I.  Q  -  

117 

118 

38. 

Average   I.    Q.    117.0. 

Examiner    

.„.      L.  W. 

L.  I.  8. 

Chronological  Age  

6-1 

6-10 

Terman  Age  

6-10 

8-4 

I.    Q  

112 

122 

39. 

Average  I.   Q.    116.6. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S. 

Chronological   Age   

7-9 

9-0 

10-0 

10-8 

11-3 

Terman  Age  

9-6 

10-6 

10-9 

12-7 

13-6 

I.    Q.    

122 

116 

107 

118 

120 

40. 

Average   I.    Q.    116.5. 

Examiner  

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  8. 

Chronological  Age  — 

8-3 

9-3 

11-4 

11-10 

Terman  Age  

8-11 

10-9 

13-3 

14-10 

I.    Q.    

108 

116 

117 

125 

41. 

Average  I.   Q.    116.2. 

Examiner  

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

Chronological   Age   

10-2 

11-9 

13-3 

13-9 

11  11 

14  1 

14—10 

16-1 

I.    Q.    

117 

119 

112 

117 

42. 

Average   I.    Q.    116.0. 

Examiner  

—  .       E.  V. 

E.  V. 

Chronological  Age  

8-11 

9-11 

Terman  Age  

10-2 

11-8 

I.    Q.    -  

114 

118 

MENTAL  GROWTH  CURVE 


27 


TABLE  VI  —  CONTINUKD 
ORIGINAL  DATA  ARRANGED  IN  ORDER  OF  MEAN  I. 

Q.—  BOYS 

43. 

Average  I.   Q.    115.5. 
Examiner  
Chronological  Age 
Terman  Age  
I.    Q.    

E.  V. 
6-10 
7-8 
.-    .          112 

E.  V. 
7-10 
9-4 
119 

44. 

Average  I.   Q.   114.6. 

Examiner  

E.  V. 

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological   Age   ... 

5-4 

5-11 

7-3 

7-11 

8-6 

Terman  Age  

5-8 

7-0 

8-6 

8-10 

10-4 

I.    Q  

106 

118 

117 

111 

121 

45. 

Average  I.    Q.   113.6. 

Examiner  

E.  V. 

E.  V. 

L.  W. 

Chronological   Age   ... 

9-2 

10-2 

11-6 

Terman  Age  

9-8 

10-10 

15-0 

I.    Q  

105 

ioa 

130 

46. 

Average  I.    Q.   113.4. 

Examiner  

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

L.  I.  S. 

Chronological  Age  ... 

5-6 

6-6 

8-1 

8-7 

9-1 

Terman  Age  

5-10 

7-4 

9-0 

10-2 

10-11 

I.   Q.   — 

106 

112 

111 

118 

120 

47. 

Average  I.    Q.   113.0. 

Examiner  

E.  V. 

8-9 

E.  V. 
9-9 

L.  W. 

11  1 

L.  I.  S. 

11-8 

L.  I.  8. 

Terman  Age   

9-7 

10-6 

12-9 

13-4 

14-8 

I.    Q.    

109 

107 

115 

114 

120 

48. 

Average  I.    Q.   112.7. 

Examiner    

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

Chronological  Age  — 

11-0 

12-7 

14-1 

14-7 

Terman  Age  

11-3 

14-10 

16-8 

16-8 

I.    Q.    

102 

117 

118 

114 

49. 

Average  I.    Q.   111.6. 

Examiner  

E.  V. 

E.  V. 

L.  W. 

Chronological  Age   — 

6-3 

7-3 

8-7 

Terman  Age  

7-2 

8-0 

9-6 

I.    Q.    -  

114 

110 

111 

50. 

Average  I.    Q.   111.5. 

Examiner  

L.  W. 

L.  I.  8. 

Chronological   Age  ... 

7-4 

8-2 

Tennan  Age  

8-4 

9-0 

I.    Q.    

113 

110 

51. 

Average  I.    Q.    111.0. 

Examiner  

M. 

L.  I.  8. 

Chronological  Age  — 

5-4 

6-7 

Terman  Age  

5-8 

7-8 

I.    Q  — 

106 

118 

52. 

Average   I.    Q.    110.5. 

Examiner  

L.  W. 

L.  I.  8. 

Chronological  Age  — 

7-4 

8-6 

Terman  Age  .. 

7-8 

9-10 

I.    Q.    —  -  

105 

lie 

53. 

Average  I.    Q.    110.0. 

Examiner  

E.  V. 

E.  V. 

L.  I.  8. 

Chronological  Age   — 

6-8 

7-8 

9-3 

Terman  Age  — 

7-0 

8-4 

10-10 

I.    Q  

105 

108 

117 

54. 

Average  I.    Q.   110.0. 

Examiner  

L.  W. 

L.  I.  S. 

Chronological   Age  — 

6-4 

7-2 

Terman  Age  

7-2 

7-8 

I.    Q  

113 

107 

56. 

Average  I.   Q.   108.7. 

Examiner  

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S. 

Chronological  Age    — 

6-4 

7-10 

8-5 

8-11 

Terman  Age  

7-0 

8-0 

9-2 

10-2 

I.   Q  

110 

102 

109 

114 

56. 

Average  I.   Q.    107.5. 

Examiner  

E.  V. 

fi-"> 

E.  V. 

7-1 

Terman  Age  

6-6 

7-10 

I.    Q.    

106 

110 

28 


IOWA  STUDIES  IN  CHILD  WELFARE 


TABLE  VI  —  CONTINUED 
ORIGINAL  DATA  ARRANGED  IN  ORDEB  OF  MEAN  I.  Q.  —  BOYS 

57. 

Average  I.    Q.    106.7. 

Examiner  

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological   Age   

5-11 

7-5 

8-1 

8-7 

Tennan  Age  

8-2 

7-10 

8-8 

9-6 

I.    Q  

104 

106 

107 

110 

58. 

Average   I.    Q.   106.7. 

Examiner    ... 

—  .       E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological  Age   

11-0 

12-2 

13-O 

13-6 

Tennan  Age  

12-0 

12-11 

14-1 

14-1 

I.    Q  

109 

106 

108 

104 

59. 

Average  I.    Q.   106.0. 

Examiner  

.  E.  V. 

E.  V. 

Chronological  Age  

11-1 

12-8 

Terman  Age  

11-6 

13-5 

I.    Q  -  

104 

108 

30. 

Average  I.   Q.    105.7. 

Examiner  

—.       E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  S. 

Chronological  Age  — 

11-2 

12-3 

14-2 

14-8 

Terman  Age  

11-1 

13-7 

14-11 

16-0 

I.    Q.    —  -  -  

99 

110 

106 

109 

61. 

Average  I.    Q.   105.6. 

Examiner  

E.  V. 

E.  V. 

L.  W. 

L.  I.  S.       L.  I.  8. 

Chronological  Age  

12-5 

13-11 

14-11 

15-4                15-10 

Terman  Age  

12-2 

14-8 

15-3 

17-2               17-8 

I.    Q  

97 

105 

102 

112                  112 

82. 

Average  I.   Q.   105.5. 

Examiner  

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  S. 

Chronological  Age   — 

5-4 

6-6 

7-6 

8-0 

Terman  Age  

5-6 

6-fl 

7-8 

9-3 

I.    Q  -  

103 

100 

103 

116 

63. 

Average  I.    Q.   105.5. 

Examiner  

E.  V. 

L.  I.  S. 

Chronological  Age  ... 

9-7 

12-0 

Terman  Age  

10-1 

12-fl 

I.    Q  

105 

106 

64. 

Average  I.    Q.    108.0. 

Examiner  

E.  V. 

L.  I.  8. 

Chronological   Age  

..    .          8-8 

11-2 

Terman  Age  

9-0 

11-5 

I.    Q.    —  -  

104 

102 

65. 

Average  I.    Q.    103.0. 

Examiner  

L.  W. 

L.  I.  8. 

Chronological  Age   ... 

10-4 

11-1 

Terman  Age  

10-5 

11-8 

I.  Q  

101 

105 

66. 

Average  I.   Q.    102.7. 

Examiner  

E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  S. 

Chronological  Age   — 

11-8 

13-3 

14-9 

15-3 

Terman  Age  

11-7 

14-1 

15-0 

15-10 

I.  Q  -  

99 

106 

102 

104 

67. 

Average  I.   Q.   102.5. 

Examiner    

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  S. 

Chronological   Age   ... 

5-5 

8-11 

7-6 

8-0 

Terman  Age  

5-6 

7-3 

7-7 

8-5 

I.    Q  

100 

104 

101 

106 

68. 

Average  I.  Q.  99.5. 

Examiner  

E.  V. 

L.  I.  8. 

Chronological  Age  ... 

6-7 

8-10 

Terman  Age  

6-8 

8-8 

I.    Q  

101 

98 

69. 

Average  I.  Q.  97.5. 

Examiner  

E.  V. 

L.  I.  S. 

L.  I.  8. 

L.  I.  i. 

Chronological  Age  ... 

7-3 

8-10 

9-3 

9-10 

Terman  Age  

7-2 

8-4 

9-2 

9-8 

I.    Q  

99 

94 

99 

98 

70. 

Average  I.  Q.  97.5. 

Examiner    

E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  8. 

Chronological  Age  ... 

10-0 

12-0 

13-10 

14-4 

Terman    Age    

10-8 

11-8 

13-1 

14-3 

I.  Q  

99 

97 

96 

90 

MENTAL  GROWTH  CURVE  29 


TABLE  VI  —  CONTINUED 
ORIGINAL  DATA  ARRANGED  IN  ORDER  OF  MEAN  I. 

Q.  —  BOYS 

71. 
72. 

Average  I.  Q.  96.0. 
Examiner  
Chronological  Age 
Terman  Age  
I.    Q.    
Average  I,  Q.  95.0. 
Examiner  
Chronological   Age   . 
Terman  Age  — 
I.    Q.    

E.  V. 
12-2 
,     .  .        11-8 
...           96 

E.  V. 
11-2 
10-1 
90 

E.  V. 
13-fl 
13-3 
90 

E.  V. 

12-9 
12-9 
100 

73. 

Average  I.    Q.   98.2. 

Examiner  

E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  S.       L.  I.  8. 

Chronological   Age    ... 

12-6 

14-1 

15-1 

15-fl               16-0 

Terman  Age  

11-0 

13-1 

14-7 

14-7               15-5 

I.    Q.    

83 

92 

96 

94                   96 

74. 

Average  I.    Q.   93.2. 

Examiner  

E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  8. 

Chronological  Age  ... 

8-7 

10-O 

10-8 

11-2 

Terman  Age  

8-3 

9-3 

9-8 

10-7 

I.    Q  

95 

92 

91 

96 

75. 

Average  I.    Q.   92.0. 

Examiner  

L.  W. 

L.  I.  8. 

Chronological  Age   ... 

-    .         10-8 

11-6 

Terman  Age  

10-2 

10-2 

I.    Q  

95 

89 

76. 

Average  I.    Q.   92.0. 

Examiner  

E.  V. 

L.  I.  S. 

OhiYinAln^lpftl     A  trt* 

9-5 

11  11 

8-6 

11  2 

I.    Q  

90 

91 

the  I.  Q.  occur.  In  order  to  illustrate  this  more  completely  the 
36  children  of  the  Five  Examination  Group  were  arranged  in  the 
order  of  merit  on  the  basis  of  the  I.  Q.  for  the  first  examination. 
For  all  of  the  children  the  first  I.  Q.  was  plotted,  Chart  Via  and 
b,  and  the  points  connected  by  a  solid  line  to  show  this  array  of 
children  in  the  original  order  of  increasing  I.  Q.  The  vertical 
scale  represents  the  range  of  I.  Q.'s  from  80  to  100.  The  numbers 
running  horizontally  across  the  chart  are  the  identification  num- 
bers of  the  children  in  the  tables  of  original  data.  The  four  suc- 
ceeding I.  Q.'s  for  each  child  were  plotted  on  the  same  vertical 
axis  as  the  point  for  the  first  I.  Q.  and  different  kinds  of  lines 
drawn  in  order  to  make  it  possible  to  identify  the  I.  Q.'s  of  dif- 
ferent children  at  the  2d,  3d,  4th  and  5th  examinations.  The 
heavy  horizontal  lines  indicate  the  conventional  classifications  of 
I.  Q.  level,  90  to  110  being  considered  average  ability;  110  to  120 
superior,  with  an  additional  classification  of  very  superior  for 
120  to  140.  In  this  study  the  very  superior  cases  were  not  suf- 
ficiently numerous  to  permit  of  the  last  classification.  Accord- 
ingly, all  children  with  a  mean  I.  Q.  of  110  or  above  are  classed  as 
superior. 


30 


IOWA  STUDIES  IN  CHILD  WELFARE 


TABLE   VII 

ORIGINAL  DATA 

ARRANGED  IN 

ORDER 

OF  MEAN 

I.   Q.  —  GIRLS 

1.    Average  I.    Q.   148.0. 

E    V 

E    V 

L    W 

LIB 

L.  I.  S. 

Chronological  

8-3 

9-4 

10-4 

11-4 
ni 

11-10 
17  7 

I.    Q  

139 

143 

158 

151 

149 

2.    Average  I.    Q.   146.8. 

Examiner  

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  8. 

Chronological  

8-11 

10-0 

11-0 

12-0 

12-5 

Terman    

12-6 

13-11 

16-7 

18-7 

18-7 

I.   Q.   -  

140 

139 

150 

155 

149 

3.    Average   I.    Q.    140.5. 

Examiner  

.     L.  I.  S. 

L.  I.  S. 

Chronological  — 

8-10 

9-7 

Terman    — 

12-7 

13-4 

I.    Q.    

142 

139 

4.    Average  I.    Q.    131.7. 

Examiner  

E.  V. 

L.  I.  S. 

L.  I.  S. 

L.  I.  S. 

Chronological 

7-0 

8-2 

8-8 

9-3 

Terman    

8-8 

10-5 

11-3 

13-6 

I.    Q.    

123 

128 

130 

146 

5.    Average  I.    Q.   130.7. 

Examiner  

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

Chronological    

9-1 

10-2 

11-8 

12-2 

Terman    — 

11-3 

12-10 

15-10 

17-8 

I.    Q  —  - 

123 

126 

136 

138 

6.    Average  I.    Q.    130.5. 

Examiner  

L.  W. 

L.  I.  8. 

fliTnTinlniyinRl 

6-4 

7-2 

Terman    

7-6 

10-3 

I.    Q.    —  -  -  

118 

143 

7.    Average  I.   Q.    130.2. 

Examiner  

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

L.  I.  S. 

Chronological  

9-6 

10-7 

12-1 

12-7 

13-0 

Terman    „ 

11-0 

13-7 

15-11 

17-8 

17-8 

I.    Q  

115 

128 

132 

140 

136 

8.    Average  I.    Q.    130.0. 

Examiner  

E.  V. 

E.  V. 

Chronological  

7-0 

8-1 

Terman    

9-2 

10-5 

I.    Q.    

131 

129 

9.    Average   I.    Q.    128.8. 

Examiner  

E.  V. 

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  8. 

Chronological  

8-10 

9-10 

11-1 

11-10 

12-4 

lfi-7 

17  1 

I.    Q  

111 

lie 

139 

140 

138 

iO.    Average  I.   Q.    127.8. 

Examiner  

E.  V, 

E.  V. 

L.  I.  S. 

L.  I.  8. 

L.  I.  S. 

Chronological 

.    ..           6-6 

7-5 

9-0 

9-6 

9-11 

Terman    

8-2 

9-2 

10-8 

12-9 

13-8 

I.    Q.    

125 

123 

119 

134 

138 

.1.    Average  I.    Q.    125.5. 

Examiner  

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S. 

«-!L_^_       l            *          I 

o_a 

10-8 

11  3 

11  10 

Terman    

10-3 

13-4 

15-1 

16-3 

I.    Q  -    -  

106 

125 

134 

137 

12.    Average  I.   Q.   125.0. 

Examiner  

—  .       E.  V. 

E.  V. 

Chronological  

.    .          8-9 

9-9 

Terman    

10-8 

12-6 

I.    Q.    —  - 

122 

128 

3.    Average  I.   Q.   124.7. 

Examiner  

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  8. 

Chronological  

4-11 

5-6 

6-6 

7-0 

Terman    

6-4 

6-10 

8-0 

8-8 

I.    Q  

128 

124 

123 

124 

14.    Average  I.   Q.    124.6. 

Examiner  

—  .       E.  V. 

L.  S. 

L.  I.  8. 

Chronological  

10-9 

12-3 

13-3 

Terman    

12-4 

15-6 

17-8 

I.    Q.    

115 

126 

133 

MENTAL  GROWTH  CURVE 


31 


ORIGINAL  DATA 

TABLE  VII  —  CONTINUED 
ARRANGED  IN  ORDER  OF  MEAN  I 

.  Q.  —  GIRLS 

15. 
16. 
17. 
18. 
19. 
20. 
21. 
22. 
23. 
24. 
25. 
26. 
27. 
28. 

Average  I.   Q.    124.0. 
Kxaniiner  .  __ 

L.  W. 

L.  I.  S. 
6-7 
8-0 
121 

L.  I.  S. 
6-9 
8-10 
131 

L.  W. 
11-2 
12  11 

L.  I.  S. 
11-11 
15-7 
130 

L.  I.  S. 
11-4 
12-3 
108 

L.  I.  S. 
14-1 

18-O 
128 

L.  I.  S. 
8-8 
10-10 
125 

L.  W. 
10-5 
12-0 
115 

L.  I.  S. 
12-6 
14-9 
118 

L.  I.  S. 
13-0 
15-5 
118 

L.  I.  8. 
10-0 
12-2 
121 

L.  I.  S. 
9-7 
10-11 
114 

L.  I.  8. 
12-5 
16-11 
136 

L.  I.  S.       L.  I.  S. 
11-9               12-3 
15-3               17-8 
129                 144 

L.  I.  S. 
14-8 
18-6 
123 

L.  I.  S. 
9-3 
11-3 
122 

L.  I.  S.       L.  I.  8. 
13-0               13-6 
16-5               17-8 
126                 127 

L.  I.  S.       L.  I.  S. 
13-5               13-11 
17-2               17-2 
127                 123 

L.  I.  8. 
10-7 
13-0 
123 

L.  I.  S. 

10-2 
12-2 
119 

Chronological  

5-9 

Term  an 

7-4 

I.    Q  

127 

Average  I.    Q.    123.5. 
Examiner  

L.  W. 

Chronological  

5-7 

Term  an 

6-6 

I.    Q.                   . 

.    .          116 

Average  I.    Q.   123.2. 
Examiner 

E.  V. 

Chronological 

9-11 

Terman 

11-0 

I.    Q  

Ill 

116 

L.  I.  S. 
6-4 
7-6 
118 

E.  V. 

9-10 
11  1 

Average  I.   Q.    122.5. 
Examiner 

L.  W. 

Chronological 

5-1 

Terman    

6-6 

I.    Q.   

..    .          127 

Average  I.   Q.    122.4. 
Examiner    

E.  V. 

Chronological    

8-9 

Terman 

10-5 

I.  Q.   

119 

112 

L.  W. 
13-1 
16-4 
124 

E.  V. 
7-6 
8-11 
119 

L.  I.  S. 
8-3 
9-6 
115 

L.  I.  S. 
7-1 
9-0 
127 

E.  V. 
8-11 
10-9 
120 

E.  V. 
11-1 
12-3 
110 

E.  V. 
11-6 
13-1 
113 

L.  I.  S. 
9-8 
11-2 
115 

L.  I.  8. 
9-2 
10-S 
116 

Average   I.    Q.   122.0. 
Examiner    

L.  I.  S. 

Chronological  

11-5 

Terman    

13-0 

I.  Q  

113 

Average  I.   Q.   121.0. 
Examiner 

E.  V. 

Chronological      

6-1 

Terman    

7-6 

I.  Q  

123 

Average  I.   Q.    120.5. 
Examiner    .       

E.  V. 

Chronological 

e-8 

Terman    

8-0 

I.    Q  

120 

Average  I.   Q.    120.0. 
Examiner    

L.  W. 

Chronological  

5-11 

Terman    - 

6-8 

I.   Q.  

113 

Average  I.    Q.    119.0. 
Examiner    

E.  V. 

Chronological    

7-10 

Terman    

9-7 

I.  Q.   

...1.          122 

Average  I.    Q.   118.6. 
Examiner    

E.  V. 

Chronological  

10-0 

Terman    

11-3 

I.    Q  

112 

Average   I.    Q.    118.0. 
Examiner    

E.  V. 

Chronological  

10-5 

Terman    

11-5 

I.   Q  ;    

109 

Average  I.    Q.    117.2. 
Examiner       

E.  V. 

Chronological  

8-0 

Terman    .     

8-10 

I.  Q.  .    

110 

Average  I.   Q.    117.2. 
Examiner    

E.  V. 

Chronological  

7-7 

Terman    

„    .          9-1 

I.    Q  

.    -          120 

32 


IOWA  STUDIES  IN  CHILD  WELFARE 


TABLE  VII  —  CONTINUED 

ORIGINAL 

DATA 

ARRANGED 

IN  OBDEB 

OF  MEAN 

I.   Q.  —  GlKLS 

29. 

Average   I.   Q. 

117.0. 

Examiner    

,_-__ 

E.  V. 

L.  w. 

L.  I.  S. 

L.  I.  S. 

Chronological  _ 

5-7 

8-9 

7-8 

8-2 

Terman    

6-8 

7-8 

9-0 

10-0 

I.  Q.  

us 

113 

117 

122 

30. 

Average  I.   Q. 

118.8. 

Examiner    

.  E.  V. 

E.  V. 

L.  W. 

L.  I.  8.       L 

.  I.  8. 

Chronological  . 

8-11 

•10-3 

11-4 

11-11 

12-* 

Terman    

10-7 

11-9 

12-1 

14-4 

15-8 

I.    Q  - 

118 

114 

108 

120 

126 

31. 

Average  I.    Q. 

iie.2. 

Examiner    

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

Chronological  . 

9-3 

10-9 

12-4 

12-10 

Term  an 

10-9 

12-5 

14-1 

15-5 

I.  Q.  

118 

115 

114 

120 

32. 

Average  I.   Q. 

116.0. 

Examiner    

....      L.  W. 

L.  I.  8 

Chronological  . 

5-11 

7-2 

Terman    

8-2 

9-2 

I.  Q  - 

104 

128 

33. 

Average  I.   Q. 

115.6. 

Examiner    .    ._ 

E.  V. 

L.  S. 

L.  I.  S. 

L.  I.  S.       L 

.  I.  S. 

5-1 

8-1 

7  7 

8-1 

o_7 

TermftrK     ,      , 

5-0 

7-4 

9-2 

9-10 

10-2 

I.  Q.   

.     -             98 

120 

121 

121 

118 

34. 

Average  I.   Q. 

115.5. 

Examiner    

....      L.  W. 

L.  I.  8 

Chronological  - 

5-4 

6-7 

Terman 

8-8 

7-2 

I.  Q.  -  

122 

109 

35. 

Average  I.   Q. 

114.5. 

Examiner    

.—      E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  S. 

Chronological  _ 

9-4 

10-6 

11-4 

11-11 

Terman    

10-10 

11-11 

12-10 

13-9 

I.  Q  

118 

114 

113 

115 

36. 

Average   I.    Q. 

113.5. 

Examiner    

.—       E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  S. 

Chronological  . 

11-8 

12-5 

13-1 

13-9 

Terman    

12-8 

13-9 

15-1 

16-7 

I.  Q  

108 

110 

115 

121 

37. 

Average  I.    Q. 

113.5. 

Examiner    

.—       E.  V. 

E.  V. 

Chronological  . 

8-1 

7-1 

Terman    

8-10 

8-2 

I.  Q  

112 

115 

38. 

Average  I.    Q. 

113.4. 

Examiner    

...       E.  V. 

L.  S. 

L.  W. 

L.  I.  S.       L 

I.  S. 

Chronological  - 

6-2 

7-1 

8-9 

9-3 

9-8 

Terman    

7-8 

8-4 

9-8 

10-3 

10-7 

I.  Q  

121 

117 

110 

110 

109 

39. 

Average  I.    Q. 

112.0. 

Examiner    

E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  8.       L 

I.  S. 

Chronological  .. 

11-4 

12-11 

14-0 

14-4 

14-10 

Terman    

11-8 

14-10 

14-10 

17-7 

17-7 

I.    Q.    . 

101 

114 

106 

122 

118 

0. 

Average  I.   Q. 

112.0. 

Examiner    

E.  V. 

E.  V. 

L.  W. 

L.  I.  S.       L 

I.  8. 

fiK—rt  nrtl  /•»  &\  no! 

a_9 

1ft-7 

11  2 

11-8 

9-4 

11  2 

12-0 

14—7 

I.    Q  

114 

109 

105 

107 

125 

41. 

Average  I.    Q. 

110.5. 

Examiner    

—      L.  W. 

L.  I.  S. 

Chronological    . 

6-8 

7-6 

Terman    

7-4 

8-4 

I.    Q  

110 

111 

42. 

Average  I.   Q. 

110.0. 

Examiner   

—       E.  V. 

L.  I.  8. 

L.  I.  S. 

L.  I.  S. 

Chronological  — 

9-4 

10-7 

10-11 

11-8 

Terman    

9-7 

10-8 

12-3 

14-7 

I.  Q  

102 

99 

112 

127 

MENTAL  GROWTH  CURVE 


ORIGIN  AL 

TABLE  VII  —  CONHNUED 
DATA  ARRANGED  IN  ORDER  OF  MEAN  I.  Q.  —  GIRLS 

43. 
44. 

45. 
46. 
47. 
48. 
49. 
50. 
51. 
52. 
53. 
54. 
55. 
50. 

Average  I.   Q. 

Examiner    _ 

100.0. 

E.  V. 
7-6 
8-4 
111 

L.  W. 
6-5 
6-8 
104 

E.  V. 
8-8 
9-7 
110 

L.  8. 

12-7 
13-8 
108 

E.  V. 
8-11 
10-2 
114 

E.  V. 

9-3 
7-0 
112 

E.  V. 
9-9 
10-4 
106 

E.  V. 
6-7 
7-0 

108 

L.  8. 
15-7 
15-3 
97 

L.  W. 

6-0 
6-6 
108 

L.  W. 

6-e 

6-10 
105 

L.  W. 
5-1 
5-8 
111 

E.  V. 

11-3 
11-1 
98 

L.  I.  8. 

9-0 
9-2 
103 

E.  V. 
8-10 
9-8 
109 

L.  I.  8. 

7-7 
8-7 
113 

E.  V. 
9-9 
10-4 
105 

L.  W. 

14-2 
15-9 
100 

L.  I.  8. 

10-3 
10-8 
104 

L.  I.  8. 
9^ 
10-1 
103 

E.  V. 
11-3 
12-* 
109 

L.  W. 
7  11 

L.  I.  8.       L.  I.  8.       L.  I.  8. 
10-1               10-6               11-0 
10-T               11-10             11-10 

Chronological  _ 

Term  an 

I.    Q.   

104                 113                 108 

L.  W. 
11-0 
12-1 
109 

L.  I.  8.       L.  I.  8. 
19-3               15-9 
16-8               19-8 
109                 109 

L.  I.  8.       L.  I.  8. 
10-8               11-2 
11-9               11-9 
108                 105 

L.  I.  S.       L.  I.  8. 
8-8                 9-9 
9-9                 9-0 
112                 105 

L.  I.  8. 

Average  I.    Q. 
Examiner    

108.5. 

Chronological  _ 

Terman    _    

I.    Q  

Average  I.   Q. 
Examiner    

108.0. 

Chronological  _ 

Terman 

I.  Q  

Average  I.   Q. 
Examiner    

108.0. 

Chronological  - 

Terman    

I.   Q.   

Average  I.   Q. 
Examiner    - 

107.7. 

Chronological  _ 

Tpirmnn 

I.  Q. 

Average  I.   Q. 
Examiner    

107.5. 

Chronological  . 
Terman    

I.  Q.  -       ..    . 

Average  I.   Q. 
Examiner    

107.5. 

Chronological  _ 

TflTtnan     , 

I.   Q. 

Average  I.    Q. 
Examined    . 

107.0. 

Chronological  - 

Terman    __ 

8-4 
105 

E.  V. 

I.    Q.    

Average  I.   Q. 
Examiner    

107.0. 

Chronological  _ 

16-9 
18-0 
112 

L.  I.  8. 

7-4 
7-8 
105 

L.  I.  8. 

7-4 
7  10 

17-8 
18-0 
118 

L.  I.  8. 

13-10 
15-10 
114 

Terman   

I.  Q.  .    

Average  I.   Q. 

Examiner    _    „ 

108.5. 

Chronological  _ 

Terman    

I.  Q.  

Average  I.   Q. 
Examiner   

106.0. 

Chronological  - 

Terman 

I.   Q  

107 

L.  I.  8. 

9-4 
9-4 
100 

E.  V. 
12-6 
13-0 
104 

L.  I.  8. 

9-0 
7-2 
100 

Average  I.   Q. 

Examiner    _ 

105.5. 

Chronological  _ 

Terman    _ 

I.    Q.    _.  

Average  I.   Q. 
Examiner   

105.3. 

Chronological  - 

Terman    . 

I.    Q  

Average  I.    Q. 
Examiner    

104.5. 

Chronological  . 

Terman    .  

I.  Q  _ 

34 


IOWA  STUDIES  IN  CHILD  WELFARE 


TABLE  VII  —  CONTINUED 

ORIGINAL  DATA 

ARRANGED  IN 

ORDER  OF 

MEAN  I. 

Q.  —  GlBLS 

57. 

Average  I.   Q.    103.5. 

Examiner    

E.  V. 

E.  V. 

L.  I.  S. 

L.  I.  S. 

Chronological  

8-8 

9-8 

11-8 

12-3 

Terman    

9-8 

10-6 

11-4 

12-2 

I.   Q.  

111 

107 

97 

99 

58. 

Average  I.   Q.    102.7. 

Examiner    

—  .       E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  S. 

Chronological  

9-2 

10-3 

12-3 

12-9 

Terman    

9-8 

10-9 

12-0 

13-3 

I.  Q  -  

105 

104 

98 

104 

59. 

Average  I.    Q.   102.6. 

Examiner    _„    „ 

E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  S.       L 

I.  8. 

Chronological  __ 

7-11 

9-0 

10-7 

10-11 

11-5 

Terman    

8-2 

9-9 

10-3 

10-9 

12-4 

I.  Q.  —  ~. 

108 

108 

98 

98 

108 

60. 

Average  I.    Q.   102.5. 

Examiner    _._    

—  .       E.  V. 

L.  I.  S. 

Chronological  

12-6 

14-10 

Terman>    

13-0 

14-11 

I.    Q.    

104 

101 

61. 

Average  I.   Q.   102.5. 

Examiner    

....      L.  W. 

L.  I.  8. 

Chronological  

8-3 

9-3 

Terman    .    

8-4 

9-7 

I.  Q  

101 

104 

62. 

Average   I.    Q.    98.5. 

Examiner    

L.  W. 

L.  I.  S. 

Chronological  

5-4 

8-6 

Terman    _  

5-2 

6-6 

I.  Q  

97 

100 

33. 

Average   I.    Q.    93.8. 

Examiner    

E.  V. 

E.  V. 

L.  I.  8. 

L.  I.  S.       L 

I.  S. 

Chronological  

9-6 

10-4 

11-6 

11-11 

12-6 

Terman    

8-8 

10-4 

10-7 

10-10 

11-10 

I.  Q.  —  

91 

100 

92 

91 

95 

64. 

Average  I.   Q.    93.5. 

Examiner    

—  -       E.  V. 

E.  V. 

Chronological  

9-8 

10-7 

Terman    

8-10 

10-2 

I.  Q.  

91 

90 

65. 

Average  I.   Q.   92.7. 

Examiner    .    

E.  V. 

L.  W. 

L.  I.  S. 

L.  I.  S. 

Ohronological 

6-4 

7-7 

8-4 

8-11 

5-10 

9-n 

7  Q 

R-K 

I.  Q  -  

92 

92 

93 

94 

86. 

Average  I.   Q.   91.7. 

Examiner    

—  .       E.  V. 

L.  W. 

L.  I.  8. 

L.  I.  S. 

Chronological  

9-3 

10-8 

11-0 

11-6 

Terman    

9-4 

9-6 

9-9 

10-2 

I.  Q.  —  -  

100 

90 

89 

88 

67. 

Average  I.   Q.    91.5. 

Examiner    

L.  W. 

L.  I.  8. 

Chronological  —  

11-2 

12-3 

Terman    

9-8 

11-9 

I.  Q  

87 

96 

It  is  apparent  that  these  class  names  have  very  little  real  sig- 
nificance, as  almost  all  of  the  children  vary  from  their  original 
classfiication  on  re-examination.  A  variation  of  only  a  few  points 
in  the  I.  Q.  measuring  actual  mental  growth  or  occurring  as  a 
chance  error  of  examination  would  be  sufficient  to  transfer  a  child 
from  the  average  to  the  superior  class.  The  same  amount  of  vari- 
ation might  keep  a  child  within  its  class  if  the  original  I.  Q.  has 
been  sufficiently  low.  This  fallacy  in  the  use  of  type  names  has 


MENTAL  GROWTH  CURVE  35 

long  been  recognized  by  careful  students  of  individual  differences, 
but  it  needs  to  be  emphasized  again  because  of  the  loose  use  of 
these  terms  by  "Binet  testers." 

Inspection  of  the  variations  in  each  child's  I.  Q.  as  shown  in 
Chart  VI  shows  that  the  original  I.  Q.  is  only  approximately  con- 
stant upon  successive  examinations.  In  two  cases  the  second, 
third,  fourth  and  fifth  I.  Q.'s  are  actually  below  the  first  I.  Q. ;  in 
five  cases  one  of  the  later  I.  Q.'s  is  below  the  original  one  and  in 
ten  cases  two  or  more  of  the  later  I.  Q.'s  are  below  the  first.  The 
remaining  19  cases  show  a  general  increase  in  I.  Q.,  though  each 
succeeding  examination  does  not  always  give  a  higher  I.  Q.  than 
the  one  preceding. 

The  uniform  and  homogeneous  nature  of  the  mean  I.  Q.  curves 
in  Chart  IV  tends  to  give  a  false  impression  of  the  individual 
child's  successive  I.  Q.'s.  For  this  reason  the  individual  curves 
of  the  36  children  who  had  the  largest  number  of  examinations 
were  plotted  in  Charts  VII  and  VIII  in  order  to  show  the  actual 
variations  in  I.  Q.  that  occur.  A  comparison  of  the  charts  for 
boys  and  girls  shows  a  greater  irregularity  of  development  in 
girls,  together  with  a  tendency  toward  greater  decrease  in  I.  Q. 
at  the  later  ages,  probably  due  to  the  fact  that  the  girls,  who  are 
more  advanced  in  their  development,  can  not  maintain  their  orig- 
inal rates  because  of  having  passed  so  many  of  the  tests  at  the 
upper  limit  of  the  scale.  The  fairly  consistent  and  uniform  curve 
which  would  correspond  to  an  absolutely  stable  I.  Q.  is  not  ex- 
emplified in  any  of  the  girls'  curves  and  in  only  two  of  the  boys' 
curves,  Nos.1  3  and  17.  A  gradual  steady  increase  in  I.  Q.  is 
observable  in  some  instances,  as  for  example  in  the  curves  of 
boys  Nos.  25,  34  and  61  and  girl  No.  5.  Examples  of  curves  show- 
ing a  steady  rise  followed  by  a  decrease  in  I.  Q.  are:  for  boys 
Nos.  11  and  8  and  for  girls  Nos.  1,  7  and  26.  Curves  showing 
marked  irregularities  with  the  I.  Q.  alternately  increasing  and  de- 
creasing are :  for  girls  Nos.  63  and  39,  and  for  boys  Nos.  47  and  33. 

"While  many  of  these  changes  are  well  within  the  5  point  limit 
of  safety,  a  sufficient  number  show  deviations  of  such  magnitude2 
that  extreme  care  should  be  exercised  about  making  any  dogmatic 
statements  in  regard  to  what  a  child's  future  status  will  be.  For 


'These   numbers    correspond   to   the   numbers    assigned    the    children    in   the   tables    of 
original  data. 

*Cf.  Root,  W.  T.     Two  Cases  Showing  Marked  Change  in  I.  Q.,  /.  of  Appl.  Ptychol., 
(5)    1921,   156-158. 


36 


SUCCESSIVE    I.Q.'S 
3 


Bi6i      G|J4     Gp»     8jJ*     Gi59     8j-»6     &44     8|4?     <S26     0:4i     G>4      Bj«    Gti5    G)40    8iib    0.7 


example,  Girl  No.  9  (Chart  VIb)  whose  I.  Q.  in  the  first  test  was 
111,  obtained  on  four  subsequent  tests  116,  139,  140  and  138.  A 
careful  study  of  this  case  showed  no  difference  in  the  method  of 
examination  and  no  unusual  physical  condition  aside  from  the 
adolescent  physiological  acceleration. 

No  doubt  these  fluctuations  in  general  mental  achievement  were 
modified  more  or  less  by  such  factors  as  time  of  day,  health  con- 
ditions at  the  time  of  the  examination,  fatigue,  interest  of  the 
child  in  a  particular  examination,  and  changes  in  the  home  and 
school  environment.  Similarly  conditioned  changes  in  attitude 
on  the  part  of  the  examiner  might  also  have  their  effect. 

2.  Deviations  of  Individuals  from  their  Mean  I.  Q,  Level.  In 
order  to  determine  other  causes  of  the  variability  that  is  apparent 
from  an  inspection  of  the  individual  I.  Q.  curves,  each  child's 
deviation  in  I.  Q.  for  every  examination  was  calculated  from  his 
mean  I.  Q.  in  all  of  his  examinations.  For  example,  one  boy  of 
very  superior  general  intelligence  showed  on  5  examinations, 
deviations  of  +.4,  — 1.6,  — 1.6  and  +3.4 ;  another  boy  of  average 
ability  showed  very  different  deviations.  It  is  possible  that  these 
deviations  are  influenced  by  chance  errors  of  examination.  Never- 
theless it  is  apparent  that  the  size  of  these  deviations  depends  not 
only  on  the  real  (inherent)  variability  of  the  child,  but  also  upon 
the  size  of  his  mean  I.  Q.  A  large  deviation  on  a  high  I.  Q.  may 


MENTAL  GROWTH  CURVE 
CHART  VIb 


37 


1            '    '            '                             A 

i 

\             ,so 

r  77  ~—"" 

A                                    >,.     /V    A, 

><J^             140 

130 


100 


90 


B|23    8(JJ     0|8      CjJO     G-19      B|I2     6(38    B|39    B|20    ftl?      Bill      6|5      GilO      &5      ft4      6il       Oi2      BiJ 
II  I  I  I  I  I  I         .1  I         1  I  I  I  I  I  I  I  80 

not  be  very  different  from  a  small  deviation  on  a  low  I.  Q.  In 
order  to  make  all  deviations  comparable  they  were  expressed  as 
percentages  of  each  child's  mean  I.  Q.  These  percentages  were 
then  averaged  for  each  child  and  the  mean  of  the  individual 


TABLE  VIII 
MEAN  OF  INDIVIDUAL  DEVIATIONS  FROM  INTELLIGENCE  QUOTIENT 

LEVEL 

Mean 

Boys 
P.  E. 

Girls 
Mean            P.  E. 

Superior  I.  Q.  110+ 
Average  I.  Q.  90-110 
Total 
Under  10  at  last  exami- 
nation 
Over  10  at  first  exami- 
nation 

4.48 
2.65 
3.99 

3.60 
4.85 

.53 
.23 
.38 

.31 
1.26 

6.92 
3.80 
5.95 

5.14 
7.09 

.78 
.29 
.57 

1.19 
1.36 

variabilities  obtained  for  various  classes  of  subjects  (Table  VIII). 
The  mean  for  all  the  boys  was  3.99  ±  .38;  for  all  of  the  girls 
5.95  ±  .57.  The  mean  for  the  superior  boys  was  4.48  ±  .53,  for 
superior  girls  6.92  ±  .78.  The  mean  for  average  boys  was  2.65  ± 
.23 ;  for  average  girls  3.80  ±  .29. 

To  determine  whether  chronological  age  was  also  a  factor  tend- 
ing to  make  the  individual  vary  from  his  I.  Q.  level,  means  were 
obtained  for  boys  and  girls  who  were  under  10  years  of  age  at 


38 


IOWA  STUDIES  IN  CHILD  WELFARE 
CHART  VII 


1       I       T 


1 — r — r 


ICO 


INDIVIDUAL  I.Q. 


100 


iU . 


the  last  examination  and  for  those  over  10  at  the  first  examina- 
tion. The  mean  for  the  boys  who  were  under  10  years  of  age  at 
their  last  measurement  was  3.60  ±  .31;  for  boys  who  were  over 
10  at  their  first  measurement  was  4.85  ±  1.26.  The  mean  for  girls 
who  were  under  10  years  of  age  at  their  last  measurement  was 

CHART  VIII 


ACF   IN  YFABS 


MENTAL  GROWTH  CURVE 


39 


5.14  ±  1.19  and  for  those  over  10  at  their  first  measurement  was 
7.09  ±  1.36. 

The  P.  E.  of  all  these  means  is  sufficiently  large  to  obscure  the 
difference  between  the  means  for  the  group  under  comparison. 
There  is,  nevertheless,  a  constant  tendency  in  all  the  groups  for 
the  girls  to  be  more  variable  than  the  boys,  for  the  superior  chil- 
dren to  be  more  variable  than  the  average  children  and  for  the 
older  children  to  be  more  variable  than  the  younger. 

3.  Differences  in  I.  Q.  at  Successive  Examinations.  One  method 
of  studying  the  stability  of  the  I.  Q.  is  that  of  direct  observation 
of  the  changes  that  take  place  on  re-examination.  For  every  pos- 
sible combination  of  examinations  in  the  four  groups  the  differ- 
ences of  I.  Q.  for  each  child  were  computed  and  the  increases  in 
I.  Q.  tabulated  as  positive  and  the  decreases  as  negative.  These 
positive  and  negative  variations  were  then  grouped  by  class  in- 
tervals of  5  point  differences  in  I.  Q.  and  the  per  cent  of  cases 
showing  each  amount  of  difference  calculated.  For  example,  16 
of  the  74  boys  who  had  two  examinations  showed  a  decrease  of 
0  to  5  points  on  the  second  examination;  i.  e.,  21.6%  showed  this 
amount  of  negative  difference.  The  percentage  distribution  of 
the  differences,  exclusive  of  the  cases  showing  no  differences,  is 
shown  for  boys  and  girls  in  Table  IX  and  Chart  IX. 

Between  the  first  and  second  examination  the  percentage  dis- 
tribution of  differences  approximates  the  normal  frequency  curve 
with  the  greatest  number  of  cases  showing  a  positive  change 
within  the  5  point  range.  As  the  interval  between  examinations 
increases  the  effect  of  the  repeated  examinations  intervening  be- 
comes apparent  in  a  shift  toward  the  positive  end  of  the  scale. 
Although  there  is  no  large  ser  difference,  the  girls  have  a  wider 
range  of  deviation,  particularly  those  of  the  Four  and  Five  Exam- 
ination Groups,  where  the  last  examination  fell  for  the  majority 
of  the  children  within  the  period  of  adolescence. 

The  mean  change  in  I.  Q.  was  found  to  be 


Examination 

1-2 

2-3 

3-4 

4-5 

Deviation 

__          i 

—         + 

—          + 

,           i 

Boys 
Girls 

4.61     7.39 
4.53     7.32 

5.12     7.60 
5.17     8.00 

3.42     7.27 
3.75     6.79 

2.50     5.14 
3.44     7.75 

Here  there  is  evident  a  shift  in  the  relation  between  negative 
and  positive  changes  as  the  number  of  examinations  children  have 
taken  grows  larger. 


40 


IOWA  STUDIES  IN  CHILD  WELFARE 


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MENTAL  GROWTH  CURVE 
CHART  IX 


41 


PERCfNTAse      DISTRIBUTION 

of    the 

DIFFERENCES    IN    I  Q 
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42 


IOWA  STUDIES  IN  CHILD  WELFARE 


These  I.  Q.  changes  cannot,  however,  be  taken  at  their  face 
value,  since  a  large  change  on  a  high  I.  Q.  may  not  be  more  signif- 
icant than  a  small  change  on  a  low  I.  Q.  In  order  to  make  all 
changes  comparable,  the  mean  gains  and  losses  from  the  first 
to  second,  second  to  third,  third  to  fourth,  and  fourth  to  fifth 
examinations  were  expressed  as  per  cents  of  the  mean  I.  Q.  at  the 
1st,  the  2d,  the  3d  or  the  4th  examination,  depending  on  the  com- 
parison being  made.  The  material  was  also  arranged  to  give  a 
separate  mean  for  average  and  superior  children.  The  per  cents 
of  change  in  I.  Q.  follow : 


Examination 

1-2 

2-3 

3-4 

4-5 

Deviation   % 

+ 

—         + 

—         + 

+         — 

Superior 
Boys 
Girls 

4.3       7.0 
3.5       8.5 

5.1         6.5 
3.5         7.1 

3.1         7.5 

4.1         5.8 

2.0         4.2 
2.5         6.3 

Average 
Boys 
Girls 

3.9      5.0 
5.0       5.5 

3.0         6.5 
6.8         6.3 

2.3         4.8 
2.9         5.7 

0            1.9 
5.0         7.0 

This  tabulation  shows  a  slightly  greater  per  cent  of  change, 
especially  in  the  positive  direction,  for  superior  children,  due 
probably  to  the  fact  that  superior  children  profit  more  readily 
by  practice. 

It  would  be  of  great  interest  to  know  what  is  the  effect  of 
chronological  age  upon  the  change  in  I.  Q.,  but  the  writers  have 
been  unable  to  devise  any  reliable  method  of  determining  the 
facts  from  the  data  available.  The  computation  of  the  mean  I.  Q. 
change  at  each  chronological  age  is  not  permissible  because  of 
the  varying  amounts  of  practice.  For  example,  at  age  8  there 
are  the  first  examinations  for  some  children,  and  also  the  second, 
third,  fourth  and  fifth  for  others.  Such  tabulation  of  cases  with 
reference  to  the  age  at  the  first  test  would,  moreover,  class  the 
children  whose  second  examination  was  given  after  a  consider- 
able time,  with  those  who  had  been  re-examined  at  a  shorter  in- 
terval, and  would  tend  to  obscure  any  characteristic  chronological 
changes  occurring.  It  would  seem  that  the  question  of  whether 
older  children  show  a  different  amount  of  I.  Q.  change  than 
younger  children  could  be  solved  only  by  a  special  experi- 
ment with  a  series  of  examinations  beginning  at  a  uniform  age, 
on  children  of  equal  intelligence,  and  applied  at  uniform  intervals. 

No  determination  can  be  made  in  this  study  of  the  effect  of  the 
interval  separating  the  examinations.  The  change  from  the  1st  to 


MENTAL  GROWTH  CURVE  43 

the  5th  I.  Q.  cannot  be  compared  with  the  change  at  other  intervals 
because  of  the  different  amounts  of  practice  intervening. 

Terman  (26)  1919,  p.  138,  used  the  method  of  I.  Q.  comparison 
described  as  follows : 

"Tests  have  been  given  to  315  children  in  the  vicinity  of  Stan- 
ford University.  To  46  of  these  children,  three  or  more  tests 
have  been  given.  In  case  of  a  child  tested  several  times  each  test 
has  been  compared  with  each  of  the  others,  for  example,  the  first 
test  with  the  second,  third,  and  fourth,  separately,  the  second 
test  with  the  third  and  fourth  separately,  and  the  third  test  with 
the  fourth.  This  gives  in  all  435  I.  Q.  comparisons." 

Terman  (26)  p.  140,  reports  that  his  comparisons  show:  "that 
it  makes  little  difference  whether  the  child  was  bright,  average 
or  dull,  how  long  an  interval  separated  the  tests  or  what  the  age 
of  the  child  was  at  the  earlier  test.  The  majority  of  the  changes 
are  for  all  groups  relatively  small .... 

"The  central  tendency  of  change  is  represented  by  an  increase 
of  1.7  in  I.  Q. :  the  middle  50%  of  change  lies  between  the  limits 
of  3.3  decrease  and  5.7  increase;  the  probable  error  of  a  predic- 
tion based  on  the  first  test  is  4.5  points  in  terms  of  I.  Q." 

The  method  of  I.  Q.  comparison  as  used  by  Terman  is  open  to 
the  objections  stated  above.  The  I.  Q.'s  obtained  after  repeated 
examinations  are  pooled  with  those  from  a  first  examination,  and 
the  average  tendency  of  change  computed  on  the  basis  of  these 
data.  It  seems  to  us  that  the  differences  in  practice  would  make 
it  inadvisable  to  pool  these  examinations. 

Such  a  tabulation  of  change  in  I.  Q.  with  reference  to  the  age 
at  the  first  test  would,  moreover,  afford  no  opportunity  for  the 
special  characteristics  of  the  adolescent  period  to  show  them- 
selves if  they  existed.  As  has  been  demonstrated  in  connection 
with  the  mental  growth  curves,  and  the  physical  growth  curves, 
boys  and  girls  have  a  period  of  adolescent  acceleration  at  differ- 
ent chronological  ages,  and  children  of  superior  and  average 
mental  and  physical  status  show  a  similar  difference.  A  pooled 
classification  of  these  different  classes  of  data  tends  to  destroy 
any  characteristic  chronological  age  changes  in  I.  Q. 

We  have  felt  that  the  solution  of  these  problems  would  not  be 
obtained  by  the  use  of  this  method.  The  695  separate  I.  Q.  com- 
parisons afforded  by  the  data  in  this  study  would  have  been  re- 
duced to  a  very  small  number  if  the  comparisons  had  been  made 
only  with  children  of  the  same  chronological  age,  sex,  I.  Q.  level, 
and  physical  status. 

4.    Intercorrelations.    The  stability  of  the  I.  Q.  can  be  investi- 


44  IOWA  STUDIES  IN  CHILD  WELFAKE 

gated  by  another  means  than  that  of  noting  the  size  of  the  differ- 
ences in  I.  Q.  and  calculating  the  central  tendency  of  change. 
The  similarity  in  the  relative  rankings  of  children  on  successive 
examinations  can  best  be  studied  by  means  of  the  method  of  cor- 
relation. Although  several  writers  have  reported  correlations 
between  two  examinations  no  data  have  so  far  been  presented  in 
the  literature  to  show  the  intercorrelations  of  several  examina- 
tions given  on  the  same  group  of  children  for  several  years.  From 
such  an  array  of  correlations  one  can  determine  whether  the  ma- 
jority of  children  maintain  at  a  later  examination  their  relative 
position  above  or  below  the  mean  of  their  group  and  tend  to 
deviate  from  this  mean  by  approximately  the  same  amount  after 
several  years  interval.  The  accuracy  of  the  prediction  is  condi- 
tioned by  the  size  of  the  correlations.  A  high  correlation  between 
the  I.  Q.'s  obtained  by  a  group  of  children  on  two  examinations 
would  mean  considerable  stability  in  I.  Q.  and  the  possibility  of 
predicting  with  a  high  degree  of  accuracy  the  future  status  of 
children  of  any  I.  Q.  level. 

For  this  method  of  investigating  the  evenness  of  the  mental 
growth  there  were  calculated  Pearson  coefficients  of  correlation 
for  four  groups  of  children.  One  group  consisted  of  56  children 
who  had  been  examined  twice;  the  coefficient  of  correlation  for 
the  two  examinations  was  +.81±.03.  Another  group  consisted 
of  51  children  who  had  been  examined  three  times ;  the  coefficient 
for  the  first  and  second  was  +.76^04;  for  the  first  and  third 
+.69  ±  .05 ;  for  the  second  and  third  +.83  ±  .03. 

It  was  possible  to  give  a  fourth  examination  to  all  but  9  of 
this  group.  The  coefficients  for  this  smaller  group  were,  for  the 
first  and  second  examinations  +.79±.04,  for  the  second  and  third 
+.86  ±  .03,  for  the  third  and  fourth  +.93  ±  .02,  for  the  first  and 
third  +.77  ±  .04,  for  the  second  and  fourth  +.82  ±  .03,  and  for 
the  first  and  fourth  +.72  ±  .05. 

The  last  group  of  36  children  was  given  five  examinations. 
The  correlation  between  the  first  and  second  was  +.85±.03, 
between  the  second  and  third  +.85±.03,  between  the  third  and 
fourth  +.91±.02,  between  the  fourth  and  fifth  +.92±.02,  be- 
tween the  first  and  third  +.74±.05,  between  the  first  and  fourth 
+.78±.04,  between  the  first  and  fifth  +.82±.04,  between  the  second 
and  fourth  +.80±.04,  between  the  second  and  fifth  +.82±.04,  and 
between  the  third  and  fifth  +.84±.03. 


MENTAL  GROWTH  CURVE 


45 


TABLE  X 

INTEBCOBBELATIONS  OF  INTELLIGENCE  QUOTIENTS  FOB  Two,  THREE,  FOUB  AND 
FIVE  EXAMINATION  GBOTTPS 

Examination 

1 
and 
2 

1 
and 
3 

2 
and 
3 

1 
and 
4 

2 
and 
4 

3 
and 

4 

1 
and 
5 

2 
and 
5 

3 

and 
5 

4 
and 
5 

5  Exam.  Group.-JCoel.  
{P.  E  

+  .85 
±.03 

+.74 
±.05 

+  .85 
±.03 

+  .78 
±.04 

+  .80 
±.04 

+  .91 
±.02 

+  .82 
±.04 

+  .82 
±.04 

+  .84 
±.03 

+  .92 
±.02 

4  Exam.  Group—  JCoel.  
(P.  E  

+  .79 
±.04 

+.77 
±.04 

+  .86 
±.03 

+.72 
±.05 

+  .82 
±.03 

+  .93 

±.02 

S  Exam.  Group-.JCoef.  
IP.  E  

+  .76 
±.04 

+  .69 
±.05 

+.83 
±.03 

i  Exam.  Group..$Coel  
(P.  E  

+.81 
±.03 

The  coefficients  (Table  X)  are  uniformly  high  and  reliable  with 
low  probable  errors,  ranging  from  +.72  ±  .05  to  +.93  ±  .02.  The 
coefficients  of  correlation  for  near-lying  examinations,  that  is, 
two  examinations  with  none  intervening,  are  highest,  the  mean 
being  +.88.  For  three  correlations  with  one  intervening  exam- 
ination the  mean  is  +.79.  For  the  two  with  two  intervening 
examinations  the  mean  is  +.80,  and  for  the  one  with  three  interven- 
ing examinations  the  correlation  is  +.82.  Although  the  coefficient 
is  highest  for  near-lying  examinations  there  is  no  tendency  for  the 
correlation  to  decrease  with  increase  of  interval. 


TABLE  XI 
PEBCENTAQE  OF  CHILDREN  TESTED  BY  SAME  EXAMINEE 

Group 

Examiner 

M£ 

•o  os 
a  x 

«w 

cog 
T3  OS 

!* 

eo  g 

•a  GO 

a  x 

*w 

M 

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59 

a  M 
<spq 

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a  H 

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v  * 
a  M 
«W 
co 

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H 

10  S 

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a  * 

«w 

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>a  os 

33 

c« 

10  S 

•O  OS 

a  x 
«H 

•*< 

5  Exam.  

E.  V  

91.4% 
0 
0 
0 

s.e 

32.2 
0 
0 
0 

99.8 

77.8 
0 
0 
0 
22.2 

28.0 
0 
0 
3.5 
67.8 

0% 
0 
0 
0 
100 

0 

0 
0 
0 
100 

0 
0 
0 
0 

100 

0% 
0 
0 
0 
100 

0 
0 
0 
18.6 
81.4 

0 
0 
0 
0 
100 

0% 
0 
0 
0 
100 

0 
0 
0 
0 
100 

0% 
0 
0 
0 
100 

0 
0 
0 
18.8 
Sl.i 

0% 
0 
0 
40 

eo 

0 
0 
0 

100 
0 

0% 
0 
0 
0 
100 

0% 
0 
0 
0 
100 

0% 
0 
0 
40 
60 

0% 
0 
0 

100 
0 

4  Exam.  
3  Exam.  
9  Exam.  

L.  8  

L.  W. 

L.  I.  8  

Mlsc  

E.  V  
L.   8  

L.  W. 

L.  I.  8  

Misc  

E.  V  
L.   8. 

L.  W.  .    . 

L.  I.  8  

Misc  

E.  V... 

L.  8  

L.  W  

L.  I.  8  

Misc  

46  IOWA  STUDIES  IN  CHILD  WELFAEE 

It  is  possible  that  the  size  of  the  correlation  might  be  influenced 
by  the  fact  that  a  number  of  children  were  examined  on  both  oc- 
casions by  the  same  examiner.  A  study  of  Table  XI  shows  that 
although  for  the  two  highest  coefficients  +.93  and  +.92,  100% 
of  the  examinations  were  made  by  the  same  examiner,  the  next 
highest  coefficient,  +.91,  showed  only  40%  by  the  same  examiner. 
Other  high  coefficients  are  +.86  with  18.6%  of  the  examinations 
and  +.85  with  91.4%  of  the  examinations  by  the  same  examiner. 
A  correlation  of  +.85  was  also  found  where  no  child  had  been 
examined  twice  by  the  same  examiner  and  a  coefficient  as  low  as 
+.76  was  obtained  with  77.8%  of  the  examinations  made  by  the 
same  examiner.  It  would  appear  then  that  the  personal  equation 
of  the  examiner  although  of  some  influence  is  not  the  important 
factor  in  the  size  of  the  correlation. 

In  general  it  is  not  justifiable  to  compute  correlations  for  a  group 
with  such  a  wide  range  in  chronological  age.  Such  a  procedure 
would  tend  to  raise  the  correlation.  The  correlations  between  I. 
Q.'s  are  probably  not  subject  to  criticism  from  this  point  of  view, 
since  the  I.  Q.  compensates  for  the  difference  in  the  chronological 
ages. 

Considerable  doubt  has  been  thrown  by  K.  Pearson  (Proc.  Roy. 
Soc.,  1897  (60)  489.)  on  the  justifiability  of  correlating  ratios. 
From  this  point  of  view  the  calculation  of  correlations  between  I. 
Q.'s  may  result  in  spurious  correlation.  This  method  is,  however, 
the  only  feasible  one  at  this  stage  in  the  development  of  the 
problem. 

In  each  group  the  highest  correlations  occur  between  near-lying 
examinations  at  the  end  of  the  series  of  examinations  where  the 
children  were  better  adjusted  to  the  situation  and  had  apparently 
reached  a  certain  stability  of  position  within  the  group. 

For  comparison  it  is  of  interest  to  note  the  size  of  the  correla- 
tions obtained  by  other  examiners.  These  were :  Bobertag,  +.95 
(Binet) ;  Terman,  +.93  (Stanford) ;  Cuneo  and  Terman,  +.95, 
+.94,  +.85  (Stanford) ;  Rosenow,  +.82  (Binet  and  Stanford) ; 
Rugg  and  Colloton,  +.84  (Stanford). 

5.  Probable  Error  of  Estimate.  Knowing  the  value  of  the 
coefficient  of  correlation  between  the  first  and  any  succeeding  test, 
we  can  predict  what  any  future  I.  Q.  would  be  and  compute  the 
difference  between  the  I.  Q.  as  predicted  and  as  actually  obtained, 
or  the  error  of  estimate. 


MENTAL  GROWTH  CURVE 


47 


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48 


IOWA  STUDIES  IN  CHILD  WELFARE 


Our  data  for  five  consecutive  examinations  of  36  children  have 
been  used  to  make  a  comparison  of  the  I.  Q.'s  actually  obtained 
and  the  I.  Q.  's  predicted  by  means  of  the  regression  equation  : 


where  y1  =  the  I.  Q.  to  be  predicted,  y  =  the  mean  of  the  obtained 
(later)  I.  Q.'s,  x  =  the  mean  of  the  obtained  first  I.  Q.'s,  xt  = 
the  individual  I.  Q.  on  the  first  test,  and  a  =  the  standard  devia- 
tion of  the  x  or  y  series. 

The  equation  can  more  conveniently  be  used  in  the  simplified 
form: 


The  quantity   r  -^     is  a  constant  through  a  whole  prediction 
* 

series,  a  different  constant  being  used  for  each  of  the  four  pre- 
diction series  (second,  third,  fourth  and  fifth  I.  Q.'s  from  first 

I.  Q.'s).    The  quantity  y  — .  r  -f-  ^  is  also  a  constant  in  each  of 

"• 

these  four  prediction  series,  which  reduces  the  formula  to  y^~ 
k(xi)-\-kl.  For  example,  by  substituting  the  constants  for  the 
prediction  of  the  second  I.  Q.  one  obtains  y1=.78(x1)-}-29.5.  For 
the  prediction  of  the  third  from  the  first  I.  Q. :  i/1=.90(a;1)-}-15.9. 


TABLE   XIII 

DISTBIBUTION  OF  DIFFEBENCES  BETWEEN  OBTAINED  AND  PREDICTED  I.  Q.'s 
(Errors  of  Estimate) 

Examination 

2345 

Amount  of 
I.  Q. 
Difference 

Number  of  Cases 

0-5 

—9 

+12 

—6 

+6 

—7 

+4 

—10 

+7 

5-10 

—4 

+  7 

—6 

+5 

—7 

+8 

—  6 

+7 

10-15 

—2 

+  1 

—2 

+5 

—3 

+3 

—  2 

+2 

15-20 

1 

0 

—3 

+2 

—1 

+2 

—  1 

0 

20-25 

0 

0 

—1 

0 

—1 

0 

0 

+  1 

MENTAL  GROWTH  CURVE 
CHART  X 


DISTRIBUTION  OF  DIFFERENCES 

BETWEEN 

OBTAINED  AND  PREDICTED    7<pV 

•5th.  Exam. 

4th  Exam, 

••MBM 

3  rd  Exam 

ind  Exam., 

-30      -<S5     -XO     -/5      -/O       -S         C       +5     +10      +15     +86     +15     +3O 

Amount    of    Difference 

For  the  prediction   of  the  fourth  from  the  first  I.   Q. :     yt= 
.90(2^)  +20.1.    For  the  prediction  of  the  fifth  from  the  first  I.  Q. : 


By  the  use  of  this  formula  the  second,  third,  fourth  and  fifth 
I.  Q.'s  for  each  child  were  predicted  and  the  differences  between 

4 


50  IOWA  STUDIES  IN  CHILD  WELFARE 

the  predicted  I.  Q.'s  and  the  I.  Q.'s  actually  obtained  at  each  of 
these  examinations  (the  errors  of  estimate)  calculated,  together 
with  the  mean  of  the  differences  for  the  group  as  a  whole.  The 
I.  Q.'s  as  actually  obtained  and  as  predicted  are  shown  in  Table 
XII.  The  distribution  of  the  differences  between  obtained  and 
predicted  I.  Q.  's  is  shown  in  Table  XIII  and  Chart  X. 

On  the  average  the  prophesied  second  I.  Q.  differs  from  the 
obtained  second  I.  Q.  by  4.7  points,  P.  E.  ±  .5,  i.  e.,  the  chances 
are  equal  that  the  average  for  the  differences  between  the  pre- 
dicted and  obtained  I.  Q.'s  will  not  be  less  than  4.2  or  greater 
than  5.4.  The  average  difference  between  the  predicted  and  ob- 
tained third  I.  Q.  or  the  average  of  the  errors  of  estimate  is  8.5 ; 
between  the  predicted  and  obtained  fourth  I.  Q.  is  7.7  and  be- 
tween the  predicted  and  obtained  fifth  I.  Q.  is  6.3.  The  mean 
interval  between  the  second  and  first  examination  was  approxi- 
mately 13  months;  between  the  third  and  first  was  28  months; 
between  the  fourth  and  first  was  36  months  and  between  the  fifth 
and  first  41  months. 

While  Table  XII  shows  for  each  prediction  series  the  most  prob- 
able predicted  I.  Q.  for  each  child,  a  better  sampling  from  a  larger 
number  of  cases  might  have  resulted  in  another  predicted  I.  Q. 
In  other  words,  while  137.9  is  the  proper  estimate  for  the  second 
I.  Q.  for  case  1,  the  probable  error  of  estimate  gives  the  number  of 
points  variation  above  or  below  this  estimate  that  will  take  in 
50%  of  all  the  other  possible  estimates.  Knowing  the  value  of 
the  4  coefficients  of  correlation  involved,  one  can  calculate  the 
probable  error  of  estimate  for  each  of  the  prediction  series  by 
means  of  the  formula  P.  E.  =  .6745  X  «  var.  V  1— r2.  This  for- 
mula gives  as  a  probable  error  of  estimate  for  the  prediction  of 
the  second  from  the  first  I.  Q.  ±4.2,  for  the  prediction  of  the  third 
from  the  first  I.  Q.  ±7.0 ;  for  the  prediction  of  the  fourth  from  the 
first  I.  Q.  ±6.2 ;  for  the  prediction  of  the  fifth  from  the  first  I.  Q. 
±5.5.  The  P.  E.  of  estimate  of  the  second  from  the  first  is  ±4.2 
as  previously  stated,  i.  e.,  the  chances  are  equal  that  the  true 
predicted  second  I.  Q.  will  not  vary  from  the  calculated  I.  Q.  by 
more  than  ±4.2.  The  chances  that  the  true  predicted  I.  Q.  will 
not  vary  from  the  calculated  I.  Q.  by  more  than  ±8.4  (or  2  P.  E.) 
are  1802  in  10,000  or  1  chance  in  every  4.5.  The  chances  that  the 
true  predicted  I.  Q.  will  not  vary  from  the  calculated  by  more 
than  ±12.6  are  434  in  10,000  or  the  chances  that  a  deviation 
greater  than  ±12.6  would  occur  are  1  in  22.  The  same  chances  of 


MENTAL  GROWTH  CURVE  51 

error  per  10,000  on  2  P.  E.  and  3  P.  E.  exist  for  the  other  predic- 
tion series,  the  only  difference  in  each  case  being  the  size  of  the 
P.  E.  The  P.  E.  of  estimate  for  the  second  examination  is  very 
nearly  the  same  as  that  reported  by  Rosenow  (20)  which  was 
3.988. 

The  size  of  the  P.  E.  obviously  depends  on  the  size  of  the  co- 
efficient of  correlation  for  the  particular  comparison  involved. 
At  first  thought  one  might  expect  that  an  increase  of  interval  be- 
tween the  examinations  would  result  in  a  larger  error  of  estimate. 
An  increase  in  the  probable  error  of  estimate  was,  in  fact,  ob- 
served to  take  place  in  the  prediction  of  the  third  from  the  first, 
where  the  interval  was  lengthened  by  one  year.  As  was  noted 
in  connection  with  the  correlations,  however,  the  coefficient  does 
not  decrease  regularly  with  an  increase  of  the  interval,  but  re- 
flects the  general  habituation  and  improvement  that  has  taken 
place  and  the  tendency  for  each  individual  to  find  and  remain  at 
his  characteristic  level. 

The  calculation  of  the  regressions  and  of  the  probable  errors 
of  estimate  is  of  no  special  significance  for  this  particular  group, 
since  the  later  I.  Q.'s  are  already  known.  The  real  value  of  the 
procedure  lies  in  utilizing  the  knowledge  in  regard  to  the  corre- 
lation between  earlier  and  later  examinations  for  predicting  the 
later  I.  Q.  of  other  children  who  have  received  only  the  earlier 
examination.  Chart  X  shows  there  is  a  conspicuous  increase  in 
the  positive  and  a  decrease  in  the  negative  differences  observable 
where  the  group  has  had  considerable  opportunity  for  becoming 
adjusted  to  the  examinations.  It  is  not  possible  from  the  data  at 
hand  to  make  an  exact  determination  of  the  amount  of  error  of 
prediction  for  various  intervals  of  examination  since  all  of  the 
children  in  this  group  have  had  repeated  measurements  in  be- 
tween, which  influences  the  size  of  the  correlations  for  the  longer 
intervals.  In  order  to  determine  how  accurately  one  may  pre- 
dict a  child's  I.  Q.  one  year  later,  two  years  later,  etc.,  the  corre- 
lations will  have  to  be  obtained  on  a  sufficient  number  of  children 
at  each  examination  interval  without  intervening  practice.  In 
the  absence  of  such  long-time  data,  one  can  say  that  it  is  possible 
to  predict  a  child's  I.  Q.  with  a  probable  error  of  from  4  to  7 
points.  Larger  amounts  of  error  would  of  course  occur  at  the 
extremes  of  distribution.  That  such  extreme  variations  do  occur 
is  shown  by  numerous  cases  in  Table  XII;  for  example  in  the 


52  IOWA  STUDIES  IN  CHILD  WELFARE 

case  of  number  10,  a  difference  of  23.2  exists  between  the  pre- 
dicted and  obtained  third  I.  Q. 

The  concept  of  a  stable  I.  Q.  involves  a  supplementary  concept 
of  a  sort  of  initial  acceleration  or  impetus  of  mental  growth 
which  predetermines  the  rate  and  level  at  which  mental  progress 
takes  place  and  results  in  an  approximately  constant  I.  Q.  The 
intelligence  quotient  could  not,  however,  remain  constant  if 
serious  fluctuations  in  the  individual's  rate  of  mental  growth 
occurred. 

If  it  should  be  proven  that  at  certain  ages  children  normally 
grow  at  an  increased  rate,  the  usefulness  of  the  I.  Q.  would  be 
considerably  limited.  It  would  always  be  of  value  still  in  de- 
termining the  relative  mental  status  of  children  of  the  same  age 
but  it  would  lose  much  of  its  prestige  as  a  convenient  diagnostic 
instrument  for  predicting  the  status  of  a  child  at  later  stages  of 
its  mental  growth.  In  a  previous  chapter  we  have  shown  that 
considerable  fluctuation  in  the  rate  of  mental  growth  occurs, 
notably  a  sharp  rise  in  the  mental  age  curve  at  the  approach  of 
adolescence.  This  general  intellectual  renaissance  is  apparently 
a  function  of  physiological  age,  occurring  earlier  in  girls  than  in 
boys  and  earlier  in  children  of  superior  intellectual  endowment 
than  in  those  of  merely  average  ability.  The  inevitable  result 
of  this  phenomenon  is  an  increased  I.  Q.  which  in  many  cases 
could  not  have  been  predicted  from  the  child's  intellectual  status 
at  an  earlier  age  and  which  would  be  a  very  unsafe  basis  in 
certain  instances  for  inferring  at  the  age  of  puberty  what  his 
earlier  I.  Q.  had  been.  Prediction  would  still  be  possible,  however, 
if  one  had  a  complete  knowledge  of  the  normal  irregularities  in 
mental  growth  at  different  ages. 

SUMMARY  AND  CONCLUSIONS 

1.  The  tabulated  results  of  individual  cases  show  that  the  I. 
Q.  is  only  approximately  constant  during  successive  examinations. 

2.  Considering  each  child's  deviation  from  his  mean  I.  Q.  ex- 
pressed as  a  per  cent  of  his  mean  I.  Q.  there  is  a  tendency  for 
the  girls  to  be  more  variable  than  the  boys,  for  the  superior  chil- 
dren to  be  more  variable  than  the  average  children,  and  for  the 
older  children  to  be  more  variable  than  the  younger. 

3.  Considering  the  difference  between  the  first  and  second  ex- 
amination the  larger  number  of  cases  show  a  difference  of  less 
than  five  points  ( —  or  -}-)  in  I.  Q-;  between  the  first  and  other 


MENTAL  GROWTH  CURVE  53 

later  examinations  with  intervening  practice,  many  more  cases 
show  greater  amounts  of  difference,  the  positive  differences  be- 
coming more  and  more  marked. 

4.  With  the  change  expressed  as  a  per  cent  of  the  previous 
I.  Q.  there  is  a  slightly  greater  change  in  the  positive  direction 
for  superior  children,  due  probably  to  the  fact  that  these  profit 
more  readily  by  practice. 

5.  No  final  determination  can  be  made  of  the  effect  of  chrono- 
logical age  or  of  the  interval  between  examinations  on  the  change 
in  I.  Q.'s. 

6.  The   coefficients   of   correlation  between  all   examinations 
within  the  four  groups  are  high  and  reliable,  ranging  from  -{-.12, 
±.05  to  -f  .93  ±.02,  showing  that  they  may  be  used  as  a  basis  for 
prediction.    The  correlations  are  probably  only  slightly  modified 
by  the  personal  equation  of  the  examiners. 

7.  The  value  of  the  probable  error  of  prediction  lies  in  utiliz- 
ing the  knowledge  in  regard  to  the  correlation  between  earlier 
and  later  examinations  for  predicting  the  later  I.  Q.  of  other  chil- 
dren who  have  received  only  the  earlier  examinations.  The  P.  E.'s  of 
estimate  range  between  4.2  and  7.0  for  the  prediction  of  the 
second,  third,  fourth  and  fifth  examination  from  the  first.  ( 

III.  THE  RELATION  BETWEEN  PHYSICAL  AND  MENTAL 

GROWTH 

1.  Data.    During  the  time  that  the  psychological  examinations 
were  being  made,  physical  measurements  and  x-ray  photographs 
were  taken  with  a  view  to  analyzing  the  physical  status  and  de- 
velopment of  the  children.    A  description  has  been  given  in  an 
earlier  study  of  the  technique  of  taking  the  height  and  weight 
measurements  and  determining  the  area  of  the  exposed  surface 
of  the  carpal  bones  which  serves  as  an  index  of  anatomical  de- 
velopment and  is  closely  related  to  the  physiological  changes  with 
their  accompanying  physical  and   mental  phenomena.     Mental 
measurements  were  also  available  for  the  children,  some  made 
on  the  same  day  as  the  physical  examinations  and  others  at  vary- 
ing intervals  with  a  few  separated  by  as  long  a  time  as  six 
months. 

2.  Resemblances  in  the  Mental  and  Physical  Development  of 
Brothers  and  Sisters.    Among  the  children  measured  in  the  school 
in  which  our  data  were  collected  there  happened  to  be  a  number 


54 


IOWA  STUDIES  IN  CHILD  WELFARE 
CHART  XI 


#99 
22* 
S06 

I9Z 

ITS 

w 
"c  160 

I 

^  144 

§> 
^  '26 

^ 

|//2 

96 
80 
64 

j 

INDIVIDUAL    HENTAL   d 
or 
BROTHERS    AND 
Mental  Growth   Curve 
for  Superior  Boyi 
for  Superior  Girlt 

family  A                Family  £ 

towTH    CURVES  / 
SISTERS        / 

/ 

J*VI 

r* 

A. 

.& 

£ 

r 

\-c*  «•- 

\ 

—  —     i 

p 

C/LJi 

*'~  > 

/ 
^ 

r-—  ^ 

\ 

Git  /»    *       *             6irfo—  -  ^— 

^ 

/ 

IB 

A 
i/j 

M 

57 

^ 

x/ 

/£ 

*f&A./ 
/ 

t 

/ 

^ 

^ 

^  A 

ao 

/ 

/ 
x? 

4'^ 

^/ 

r 

/ 

// 

ffl</' 

2 

? 

) 

£4 

2 

^Xj 

g 

« 

tf 

n 

16 
\ 

9          10          II 
i  in   Years, 


15         16 


who  were  related  to  each  other.  Chart1  XI  shows  the  individual 
mental  growth  curves  of  two  families  in  each  of  which  three 
members  had  been  given  repeated  measurements.  Family  A  in- 
cludes a  boy  No.2  3,  and  two  girls,  Nos.  2  and  20,  two  of  whom 
are  superior  to  the  mean  for  the  superior  children  of  this  study. 
Family  B  includes  two  boys,  Nos.  10  and  40,  and  one  girl,  No.  39. 
These  children  are  closer  to  the  mean,  and  the  girl  is  below  it  for 
a  considerable  part  of  its  course.  The  members  of  Family  A 
show  a  certain  resemblance  in  the  smooth  and  even  rise  of  their 
growth  curves,  whereas  the  curves  for  Family  B  are  more  irregu- 
lar and  L.  B.  even  shows  periods  of  no  measureable  mental 
growth.  There  will  be  noted  a  similarity  in  the  general  trend 


"The  norms  on  this  chart  are  the  mean  for  the  superior  and  average  children  in  this 
study. 

2These  numbers  correspond  to  those  assigned  to  individuals  in  the  tables  of  original 
data. 


MENTAL  GROWTH  CURVE 


55 


of  the  mental  growth  curves  of  the  brothers  in  Family  B,  and 
also  of  the  sisters  in  Family  A. 

3.  Mean  Mental  Age  of  Physiologically  Accelerated  and  Re- 
tarded Children.  The  children  included  in  this  study  were  di- 
vided into  4  groups  on  the  basis  of  general  physical  development. 
Group  1  consisted  of  the  boys  whose  height  and  weight  were 
above  the  norms  for  their  age,  and  Group  2  of  the  boys  whose 
height  and  weight  were  below  the  norms,  or  very  close  to  the 
norms  in  one  or  the  other  of  these  two  measurements.  Group  1 
consisted  then  of  physiologically  accelerated  boys  and  Group  2 
of  physiologically  retarded  boys,  since  it  has  been  shown  by  Bald- 
win (1)  and  (3),  that  height  and  weight  are  closely  correlated 
with  physiological  maturation.  This  division  was  made  on  the 
basis  of  the  physical  measurements  without  knowledge  of  the 
mental  age  of  the  child.  A  similar  division  into  two  groups  was 
made  for  the  girls. 

The  corrected  mental  ages  of  the  children  in  each  of  the  four 
groups  were  then  averaged  for  each  chronological  age  as  shown 
in  Table  XIV.  The  mean  mental  age  of  physiologically  acceler- 


TABLE  XIV 

MEAN  MENTAL  AGE  IN  MONTHS  OF  PHYSIOLOGICALLY  ACCELERATED  AND 

RETARDED  BOYS  AND  GIRLS 

Chronological 

Boys 

Girls 

Age 

Accelerated 

Retarded 

Accelerated 

Retarded 

5 

72.0 

62.8 

74.4 

57.6 

6 

89.4 

83.2 

81.3 

79.0 

7 

101.3 

97.1 

99.9 

95.0 

8 

118.2 

110.8 

114.6 

107.0 

9 

131.1 

120.3 

128.6 

119.1 

10 

142.4 

131.0 

141.1 

131.0 

11 

155.3 

137.6 

151.2 

144.3 

12 

171.1 

150.1 

176.7 

168.2 

13 

179.0 

158.4 

(182.5) 

189.2 

14 

194.2 

166.2 

194.9 

183.7 

ated  boys  is  uniformly  higher  than  the  mean  mental  age  of  re- 
tarded boys.  For  the  girls  the  same  holds  true  with  the  exception 
of  age  13,  where  the  mean  (printed  in  parenthesis)  is  too  low 
because  of  the  inclusion  of  the  measurements  of  some  girls  who 
were  of  superior  intellectual  ability  but  of  the  very  tall,  thin  type. 
This  table  confirms  the  findings  of  other  investigators  summar- 
ized in  (2),  who  in  general  agree  that  superior  mental  develop- 
ment accompanies  superior  physical  development  as  a  rule.  The 
first  investigation  to  trace  the  correspondence  between  pedagog- 


56  IOWA  STUDIES  IN  CHILD  WELFARE 

ical  acceleration  and  physical  development  by  means  of  consecu- 
tive school  marks  and  physical  measurements  was  made  by  Bald- 
win (1)  in  1914.  The  present  study  is  the  first  to  determine  for 
the  same  individuals  the  relation  between  general  physical  status 
and  mental  growth  as  indicated  by  consecutive  intelligence 
examinations. 

4.  The  Relation  between  Physical  Traits  and  Mental  Age.  A 
correlation  between  height  and  mental  age  previously  reported 
by  Baldwin  (2)  was  +.71±.04  for  boys  and  +.62±.05  for  girls.  In 
the  present  study  the  particular  mental  age  selected  for  each  child 
was  the  one  which  had  been  determined  nearest  to  the  time  of 
physical  measurement.  In  no  case  was  there  more  than  a  few 
months  interval  between  the  physical  and  mental  measurement. 
The  correlations  obtained  between  height  and  mental  age  are  for 
72  boys  +.84  ±02,  and  for  61  girls  +.89  ±.02.  The  correlation 
between  weight  and  mental  age  by  Baldwin  (2)  was  for  boys 
+.68  ±.04  and  for  girls  +.56  ±.06.  In  the  present  study  the  cor- 
relations for  weight  and  mental  age  are  higher,  that  is,  for  boys 
+.86±.02  and  for  girls  +.77±.04. 

The  significance  of  the  growth  of  the  carpal  bones  in  rela- 
tion to  general  physical  development  was  first  emphasized  by 
Kotch  in  1910  and  is  summarized  by  Baldwin  (3).  In  order  to 
determine  the  relationship  between  anatomical  age  as  indicated 
by  the  comparative  development  of  the  carpal  bones  and  mental 
development  as  shown  by  the  mental  age  rating,  Pearson  coef- 
ficients of  correlation  have  been  worked  out  by  us.  These  coef- 
ficients give  the  first  determination  of  the  interdependence  of 
these  physical  and  mental  traits.  The  coefficient  of  correlation 
between  mental  age  and  an  index  of  anatomical  age,  (exposed 
area  of  the  carpal  bones  of  the  right  wrist)  was  for  54  boys 
+.873  ±.021 ;  for  50  girls  +.869  ±.023. 

Earlier  correlations  between  height  and  weight  and  the  exposed 
area  of  carpal  bones  for  a  group  of  children  were  reported  by  Bald- 
win (3).  The  correlations  between  height  and  total  exposed  area 
of  carpal  bones  of  the  right  wrist  were  for  boys  +.88  ±.03  and 
for  girls  +.73  ±.05.  The  correlation  between  weight  and  area  of 
carpal  bones  was  for  boys  +.76  ±.05  and  for  girls  +.77  ±.05.  For 
this  study  the  correlations  between  height  and  weight  for  boys 
was  +.92  ±.01,  and  for  girls  +.89  ±.02. 

As  has  previously  been  pointed  out  by  Baldwin  (2)  the  size  of 
these  coefficients  is  increased  by  the  wide  range  of  ages.  It  is 


MENTAL  GROWTH  CURVE 


57 


possible  to  gain  some  knowledge  of  the  influence  of  the  age  factor 
by  the  method  of  partial  correlation.  The  results  for  49  girls 
selected  because  of  the  completeness  of  the  data,  show  the  follow- 
ing intercorrelations  of  height,  weight,  X-Rays,  mental  and  chrono- 
logical age.  /  / 


TABLE  XV 
INTEBCORRELATIONS  BETWEEN  PHYSICAL  TRAITS,  CHRONOLOGICAL  AND 
MENTAL  AGE 

Chr.  Age 

Weight 

Height 

Mental  Age 

Age 
Weight 
Height 
Mental  Age 
X-Ray 

.84 

.88 
.88 
.92 

.86 
.71 
.88 

.89 
.92 

.83 

The  partial  correlations  with  one  factor  constant  for  these  same 
girls  are  given  in  Table  XVI. 


TABLE  XVI 
PARTIAL  CORRELATIONS  BETWEEN  PHYSICAL  TRAITS,  CHRONOLOGICAL  AND 
MENTAL  AGE 

Traits 

Constants 

Chron. 
Age 

Mental 
Age 

Height 

Weight 

X-Ray 

Height-Weight 
Height-Car.  Age 
Height-Ment.  Age 
Height-X-Ray 
Weight-Chr.  Age 
Weight-Ment.  Age 
Weight-X-Ray 
X-Ray-Chr.  Age 
X-Ray-Ment.  Age 
Chr.-Ment.  Age 

.57 

.53 
.62 

—.15 
.52 

.09 

.80 
.41 

.73 
.66 

.76 
.72 

.30 
—.40 
.37 
.62 
.04 
.47 

.52 
.81 
.65 

.71 
.63 
.76 

.38 
.16 
.59 

.14 
—.11 

.54 

The  influence  of  chronological  age  is  more  important  with  some 
traits  than  others.  For  example  the  correlations  between  physical 
traits  are  very  little  influenced  by  keeping  chronological  age  con- 
stant (+.89  to  -f.53).  Although  there  is  no  correlation  between 
weight  or  X-Rays  and  mental  age  for  this  group  when  chronolog- 
ical age  is  kept  constant,  there  is  a  positive  correlation  between 
height  and  mental  age. 


58  IOWA  STUDIES  IN  CHILD  WELFARE 

SUMMARY  AND  CONCLUSIONS 

1.  There  is  a  similarity  in  the  mental  growth  curves  of  broth- 
ers and  sisters.     The  resemblance  between  brothers  and  sisters  is 
further  shown  in  physical  traits  by  the  correlation  of  the  height 
X-Eay  and  weight  quotients  and  in  mental  traits  by  the  corre- 
lation between  the  I.  Q.'s.    The  correlations  are  higher  for  the 
physical  traits  than  for  the  mental. 

2.  The    mean    mental    age    of    physiologically    accelerated    is 
higher  than  the  mean  mental  age  of  physiologically  retarded  chil- 
dren.   This  study  is  the  first  to  determine  for  the  same  individuals 
the  relation  between  general  physical  status  and  mental  growth 
as  determined  by  consecutive  intelligence  examinations. 

3.  The  coefficients  of  correlation  between  height  and  mental 
age  are  high  even  when  the  influence  of  chronological  age  is  elim- 
inated. 

IV.    GENERAL  CONCLUSIONS 

For  years  the  literature  has  been  full  of  statements  in  regard 
to  the  desirability  of  obtaining  repeated  measurements  on  the 
same  children  in  order  to  study  the  process  of  mental  develop- 
ment. The  use  of  the  Stanford  Revision  of  the  Binet  scale  even 
for  the  relatively  short  period  of  four  years  shows  the  unsuita- 
bility  of  this  scale  in  its  present  form  as  a  means  for  measuring 
mental  growth.  The  limited  number  of  alternative  tests  results 
in  a  certain  practice  effect  on  repeated  examinations.  Another 
defect  of  the  present  system  of  tests  is  the  lack  of  a  sufficient 
number  of  tests  at  the  higher  levels  to  measure  the  mental  growth 
that  apparently  goes  on  in  a  bright  young  child  even  after  the 
exhaustion  of  the  16  or  18  year  old  tests.  It  is  commonplace  in 
clinical  psychology  that  a  gifted  child  has  more  opportunity  to 
gain  a  high  I.  Q.  if  measured  early  in  his  life  where  he  has  a 
greater  range  of  tests  in  which  to  succeed.  Theoretically  it  would 
seem  to  be  a  better  measure  of  mental  growth  to  use  a  combina- 
tion of  point  scales  for  specific  mental  traits,  each  scale  to  be  suf- 
ficiently extended  to  measure  whatever  ability  exists  and  the  whole 
system  to  include  a  sufficient  variety  of  traits  to  afford  a  general 
measure  of  the  development  of  the  individual. 

The  findings  of  this  study  have  been  summarized  in  detail  at 
the  end  of  each  section.  A  survey  of  these  results  show  the  im- 
portance of  many  factors  influencing  mental  growth  processes, 


MENTAL  GROWTH  CURVE  59 

and  producing  differences  in  the  mental  growth  curves  of  boys 
and  girls,  and  of  children  of  superior  and  average  ability. 

An  analysis  of  the  individual  growth  curves  shows  that  the  I. 
Q.  is  only  approximately  constant  during  successive  examinations. 
The  amount  of  difference  between  I.  Q.'s  obtained  at  various  ex- 
aminations is  sufficiently  small,  and  the  correlations  between  the 
examinations  are  sufficiently  high  with  small  probable  errors  of 
estimate,  to  permit  of  predicting  from  an  earlier  examination 
what  the  individual's  later  development  will  be. 

The  most  significant  outcome  of  this  study  is  the  empirical  de- 
termination of  the  mental  growth  curve  and  the  establishment  of 
the  close  interrelation  between  mental  and  physical  development 
as  shown  by  the  general  similarity  between  growth  in  height  and 
in  mental  age,  the  rise  in  the  mental  age  curve  at  the  adolescent 
years,  the  superior  mental  development  of  physiologically  accel- 
erated children,  and  the  high  correlation  between  mental  age  and 
height. 

It  is  evident  that  mental  age  ratings  by  the  present  scale  are  the 
result  not  only  of  native  intelligence  but  also  of  the  degree  of 
physiological  acceleration  over  that  which  is  normal  for  the  age. 
This  latter  factor  is  of  extreme  importance  in  any  educational  or 
social  treatment  of  the  individual.  A  high  I.  Q.  reflects  this  fac- 
tor as  well  as  the  general  intelligence  that  it  is  designed  to 
measure. 


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